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Sliding Block Puzzles, Part 3
Earlier, I introduced the most difficult title candidate for a puzzle with one A-Diagonal-Traverse in 4x4. Fortunately, the puzzle search engine eliminated all errors, proved that 132 hands were the biggest trouble in an inner 4x4 puzzle without inner walls!
(There is not a lot of clarifications).
While the reader is waiting, the main results of 4x4 search are shown in this notebook. Apart from this, we will talk about how the methods that are very simple in the past work and the guidelines for all kinds of work time. In order to determine the difficulty of SBP, all kinds of statistics will be examined, and new measurement standards will be presented.
Search Results
SbpSearcher was launched in all puzzles and borrowed 4x4 puzzles within 3 hours (12295564 puzzles). The following is the best simple^3 4 × 4 N-Valent SBP (N is 1 to 15):
Click to see the full text
And for the comparison, it shows the number of steps compared to the ted to the above:
1 4 9 9 36 51 62 62 89 132 81 64 25 21 1 4 9 24 36 52 68 90 132 81 64 73 61 25 21
All notes at the top line of the table are equal to the corresponding entry at the bottom line of the table, and some notes (for example, p = 7 or p = 4) Note that it is smaller. This is the previous intelligence (in effect, it was activated as a sub function of the puzzle Evolver using slide blocks), and the first right, the bottom, the right, the right, throughout the board. It can be explained from the fact that the figure that moved below was defined as a motivated figure. In this method, intelligence includes all the 4x4 simple^3 puzzles, for example, the upper left square is empty, but the motivated figure includes a puzzle with a puzzle that is often found in one square! You can now explain the case of 6 shapes and the case of the eight shapes (the target figure in the upper left square is the first hand), but what about the other two cases? < Span> Earlier, I introduced the most difficult title candidate for a puzzle with one A-Diagonal-Traverse in 4x4. Fortunately, the puzzle search engine eliminated all errors, proved that 132 hands were the biggest trouble in an inner 4x4 puzzle without inner walls!
(There is not a lot of clarifications).
While the reader is waiting, the main results of 4x4 search are shown in this notebook. Apart from this, we will talk about how the methods that are very simple in the past work and the guidelines for all kinds of work time. In order to determine the difficulty of SBP, all kinds of statistics will be examined, and new measurement standards will be presented.
SbpSearcher was launched in all puzzles and borrowed 4x4 puzzles within 3 hours (12295564 puzzles). The following is the best simple^3 4 × 4 N-Valent SBP (N is 1 to 15):
Click to see the full text
And for the comparison, it shows the number of steps compared to the ted to the above:
The Algorithm, In Slightly More Detail Than Last Time
1 4 9 9 36 51 62 62 89 132 81 64 25 21 1 4 9 24 36 52 68 90 132 81 64 73 61 25 21
All notes at the top line of the table are equal to the corresponding entry at the bottom line of the table, and some notes (for example, p = 7 or p = 4) Note that it is smaller. This is the previous intelligence (in effect, it was activated as a sub function of the puzzle Evolver using slide blocks), and the first right, the bottom, the right, the right, throughout the board. It can be explained from the fact that the figure that moved below was defined as a motivated figure. In this method, intelligence includes all the 4x4 simple^3 puzzles, for example, the upper left square is empty, but the motivated figure includes a puzzle with a puzzle that is often found in one square! You can now explain the case of 6 shapes and the case of the eight shapes (the target figure in the upper left square is the first hand), but what about the other two cases? Earlier, I introduced the most difficult title candidate for a puzzle with one A-Diagonal-Traverse in 4x4. Fortunately, the puzzle search engine eliminated all errors, proved that 132 hands were the biggest trouble in an inner 4x4 puzzle without inner walls!
(There is not a lot of clarifications).
While the reader is waiting, the main results of 4x4 search are shown in this notebook. Apart from this, we will talk about how the methods that are very simple in the past work and the guidelines for all kinds of work time. In order to determine the difficulty of SBP, all kinds of statistics will be examined, and new measurement standards will be presented. SbpSearcher was launched in all puzzles and borrowed 4x4 puzzles within 3 hours (12295564 puzzles). The following is the best simple^3 4 × 4 N-Valent SBP (N is 1 to 15): Click to see the full text In fact, as mentioned above, simple puzzles are defined as follows: "Puzzle using slide blocks, the figure to move to the target is in the upper left corner, and the goal is the lower right of the board. It is to move the figure to the corner of. " Unfortunately, the question of when the figure is in the lower right corner of the go board has an ambiguous point. Is it when the square in the lower right corner is occupied by the target target, or when the target figure is as far as possible in the lower right corner? If the latter, when solving some problems, more ambiguity will occur. Which figure has moved to the right right now? SbpSearcher uses the previous definition for such a problem. In other words, a puzzle whose target element is R-shaped is not processed. (In fact, this check is performed when Sbpfinder can solve the puzzle in the just state). If the initial definition is stricter than the second definition, SbpSearcher can only search for "Strict Simple Puzzle 4x4 Sliding Block Puzzle". Except for the case of P = 7, the result will not change, but it will be worthwhile to change the version of the SbpSearcher and operate even a no n-strict simple puzzle using a sliding block. < SPAN> In the case of 4 shapes, the initially announced puzzle (here is the entire list) is not Simple^3, but cannot be Simple^3 SBP, which sortes the blocks within 5 hands. Interestingly, the new fou r-digit "Best" puzzle has just changed the block shift, target figure, and target position to James Stevens's "Simple"! (The puzzle of this article is a public property except for the upper right of this image, unless there is a copyright problem, so it is a public property, except for the upper right of this image). It is impossible to solve the puzzles of the seven parts of 68Moves! The triomino in the upper left must be rotated vertically and placed. I think it's a type mistake, but there are doubts. Why do you make a difference with 6 hands? In fact, as mentioned above, simple puzzles are defined as follows: "Puzzle using slide blocks, the figure to move to the target is in the upper left corner, and the goal is the lower right of the board. It is to move the figure to the corner of. " Unfortunately, the question of when the figure is in the lower right corner of the go board has an ambiguous point. Is it when the square in the lower right corner is occupied by the target target, or when the target figure is as far as possible in the lower right corner? If the latter, when solving some problems, more ambiguity will occur. Which figure has moved to the right right now? SbpSearcher uses the previous definition for such a problem. In other words, a puzzle whose target element is R-shaped is not processed. (In fact, this check is performed when Sbpfinder can solve the puzzle in the just state). If the initial definition is stricter than the second definition, SbpSearcher can only search for "Strict Simple Puzzle 4x4 Sliding Block Puzzle". Except for the case of P = 7, the result will not change, but it will be worthwhile to change the version of the SbpSearcher and operate even a no n-strict simple puzzle using a sliding block. The 13th part is similar to the time puzzle that is introduced in the Hodan book in the Hodarn book! (See also articles about this in Rob Stickman's work collection) Except for this, there is still the effect of decomposing parts, sorting parts, and creating auxiliary movements, but it has been selected. For that. Among the entire SBP programs, there are only two "neat" methods: Sbpfinder and SbpSearcher. The former uses a sliding block placed on the NXM grid to explore all the possible positions of the "just solved" puzzle. (N-1)*(M-1)) (Experienced speculation. Due to the nature of this method, it is considered difficult to calculate the execution time). First, give the grid as follows: 0 1 3 6 10 2 4 7 7 11 15 8 12 16 19 9 13 17 22 14 18 21 23 23 Here, the numbers increase from the upper right to the lower left, and as soon as the road hits left or down, it moves to the next column. (Technical note: In the case of a square grid, the formula is x+y Next, start this method from cell#0 and prepare as follows: Think of a board with a hole partly: (In cell 0, this board is full of holes) Take all the meanings of the cells from (Cell_number 1) to the cell number on the left, and arrange them in List A. Remove all the duplication of A. If there is no correct value in A, add the meaning of 0 (alternative hole) and the smaller meaning from 1 to 4 not found in A (if there is no meaning from 1 to 4). Nothing other than). Execute the filling code function (that is, the current function), submit it into the cell number +1, and the meaning of the N of A is passed to the level of the function whose cell number is changed to N. Execute. However, if the board is completely buried (that is, Cell_number = 25), check if there is a gap there and whether it has just been resolved, and if so, the piece number is standardized and given first. Confirm that you have not encountered a thing, and if so, sort the board with the correct "box" of the piece number. After the method of filling the board is over, there should be a box of N*M-1 and can be placed on the N*M grid, all that may have been decided! The presenter needs to generate all possible methods that are likely to be placed on the grid of the same volume of the grid of the Nx M grid. For example, it is possible to select all of the potential fiv e-color grid options (4 colors and holes) and send duplicate, but this is actually 4 (5^(n*m)). × 4 It is unlikely that the possibility of the recording of the grid is close to reality. In this method, it is possible to generate the correct number of figures based on the current number of figures and the highly possible curves and determination of all of the NXM grids, and then the consequences of the number of shapes. However, it may have been added to the results of the current step, which lends O (single_piece_results*all_justsolved_results). However, this amount may be a small rise if you care about the actual number of 4x4 grids (Single_piece_results = 11505, All_justsold_results = 12295564), and the expected work time has been a 5-Coloring luxury. It is almost the same as the method. However, it is possible to speed up this method, and it can reduce the number of fragments that need to be discovered rather than the probability of adding various tricks. After all, it is possible to sort all likely options for the side that separates the digits and find out which girder is regarded as a hole. Depending on the location, the time is Inter-O (2^(3nm-n-m)) or O (2nm-n-m)), but the first version is clearly impossible, 2 I In fact, Fillboard-Method needs to find a board that is about 1, 5 times the expected number of boards to guarantee that he has not found them before, and in effect 4 × 4 Grid's hash tables lead to 500 million calls. The second method where Sbpsearcher is almost completely made is simpler! It starts with a solved puzzle (this has the ability to be generated by the Fillboard method) and the de facto list that is generated for each board in the list: Execute the intelligence of the diameter from the current puzzle and find the target figure in which position in the current puzzle numbers; Wa (a_i+2, i = 1-n) (equation 1) Here, N is the number of subsidiaries, and A_I is the complexity of I, the II HUZLA. Furthermore, if Node A is between the original node and the last node, the complexity of A may be calculated as follows. A_n+1+1/2 SOM (a_i+2, i = 1-n -1) (equation 2) < SPAN> Nick Baxter and I are about to close the difficulty of moving from a certain point to another point. I am working on the metrics I need. The main idea is that the complexity of Node A in columns in column is almost equal to the average difficulty reaching Node A in all straight trees in the column. However, it is not obvious to seek the difficulty of reaching Node A to Node B in a tree. For example, let's look at the first view. For example, let's say you are at the entrance of the maze and the maze itself is quite far and high. If you understand that the labyrinth is actually a tree (that is, there is no loop), it is a wise way to pass through this part of the labyrinth no matter which way you choose. When returning to the first node from this part, this part does not have a target node, so it means that you can choose another random road (of course, so it is already walking. It doesn't fit). (In fact, paying for this, you need to do all the methods for you to believe that the goal of the target is in any of the maze: one method Return to it). On the other hand, whatever the complexity of the maze is, we must go to see if you reach the goal of the target or to judge that there is no goal in the maze. The average number of stems (the complexity is given a way to go down and up as +2). If the node you are, if there is no storage unit that will be the goal of the goal, you need to pass through all the paths, so the most important Node A from this node has the ability to calculate as follows. I am. Wa (a_i+2, i = 1-n) (equation 1) Here, N is the number of subsidiaries, and A_I is the complexity of I, the II HUZLA. Furthermore, if Node A is between the original node and the last node, the complexity of A may be calculated as follows. A_n+1+1/2 SOM (a_i+2, i = 1-n -1) (equation 2) Nick Baxter and I need to close the difficulty level of moving from a certain point to another point. I am working on a metric. The main idea is that the complexity of Node A in columns in column is almost equal to the average difficulty reaching Node A in all straight trees in the column. However, it is not obvious to seek the difficulty of reaching Node A to Node B in a tree. For example, let's look at the first view. For example, let's say you are at the entrance of the maze and the maze itself is quite far and high. If you understand that the labyrinth is actually a tree (that is, there is no loop), it is a wise way to pass through this part of the labyrinth no matter which way you choose. When returning to the first node from this part, this part does not have a target node, so it means that you can choose another random road (of course, so it is already walking. It doesn't fit). (In fact, paying for this, you need to do all the methods for you to believe that the goal of the target is in any of the maze: one method Return to it). On the other hand, whatever the complexity of the maze is, we must go to see if you reach the goal of the target or to judge that there is no goal in the maze. The average number of stems (the complexity is given a way to go down and up as +2). If the node you are, if there is no storage unit that will be the goal of the goal, you need to pass through all the paths, so the most important Node A from this node has the ability to calculate as follows. I am. Wa (a_i+2, i = 1-n) (equation 1) Here, N is the number of subsidiaries, and A_I is the complexity of I, the II HUZLA. Furthermore, if Node A is between the original node and the last node, the complexity of A may be calculated as follows. A_n+1+1/2 SOM (a_i+2, i = 1-n -1) (equation 2) Here, A_N is a coordination that leads to the goal. In other words, half of the goal and the route to the goal must be averaged. Since the difficulty level of the root node is assumed to be 0, it is only necessary to fill the complexity of the node as the tree is moved in order from the bottom. After calculating the complexity of the root node, the length of the route between the initial nodes and the final node needs to be deducted, so the complexity of the labyrinth (the only labyrinth) becomes BB and is equal to 0. Surprisingly, using this scheme can see that the complexity of a tree with one target node is always measured as V-1-M. Here, V is the number of wood nodes (V-1 is the number of ribs, but this is incorrect in the graph), and M is the number of steps to reach the final node from the early wood node. Therefore, the complexity of transition from the graph in BB-METRIC to another point is that the average length of the initial peak and the final peak of the count is subtracted from the number of the peaks and the last peak. Equivalent to. You need to pay attention to several points (and give up your responsibilities): First, the actual graph of which position can reach each other with one action depends on the type of stroke. -Metric is a six competitors that do not actually solve the problem! Second, it is very difficult to solve the problem of calculating the average route length between the two columns. In particular, in the algorithm, which gives the maximum route length between the two points in a multiple time, it is possible to check whether the number of Hamilton has a route exceeding the percentage time. Since the Hamilton route problem is NP-FULL, the problem of the seller, the problem of the bag, and the color of the count can be solved. At mult i-section time! Finally, I have not yet confirmed this statistics in the actual puzzle, and no one has come up with the same complex statistics. If anyone knows, please let me know! < SPAN> Here, A_N is a coordination that leads to the goal. In other words, half of the goal and the route to the goal must be averaged. Since the difficulty level of the root node is assumed to be 0, it is only necessary to fill the complexity of the node as the tree is moved in order from the bottom. After calculating the complexity of the root node, the length of the route between the initial nodes and the final node needs to be deducted, so the complexity of the labyrinth (the only labyrinth) becomes BB and is equal to 0. Surprisingly, using this scheme can see that the complexity of a tree with one target node is always measured as V-1-M. Here, V is the number of wood nodes (V-1 is the number of ribs, but this is incorrect in the graph), and M is the number of steps to reach the final node from the early wood node. Therefore, the complexity of transition from the graph in BB-METRIC to another point is that the average length of the initial peak and the final peak of the count is subtracted from the number of the peaks and the last peak. Equivalent to. You need to pay attention to several points (and give up your responsibilities): First, the actual graph of which position can reach each other with one action depends on the type of stroke. -Metric is a six competitors that do not actually solve the problem! Second, it is very difficult to solve the problem of calculating the average route length between the two columns. In particular, in the algorithm, which gives the maximum route length between the two points in a multiple time, it is possible to check whether the number of Hamilton has a route exceeding the percentage time. Since the Hamilton route problem is NP-FULL, the problem of the seller, the problem of the bag, and the color of the count can be solved. At mult i-section time! Finally, I have not yet confirmed this statistics in the actual puzzle, and no one has come up with the same complex statistics. If anyone knows, please let me know! Here, A_N is a coordination that leads to the goal. In other words, half of the goal and the route to the goal must be averaged. Since the difficulty level of the root node is assumed to be 0, it is only necessary to fill the complexity of the node as the tree is moved in order from the bottom. After calculating the complexity of the root node, the length of the route between the initial nodes and the final node needs to be deducted, so the complexity of the labyrinth (the only labyrinth) becomes BB and is equal to 0. Surprisingly, using this scheme can see that the complexity of a tree with one target node is always measured as V-1-M. Here, V is the number of wood nodes (V-1 is the number of ribs, but this is incorrect in the graph), and M is the number of steps to reach the final node from the early wood node. Therefore, the complexity of transition from the graph in BB-METRIC to another point is that the average length of the initial peak and the final peak of the count is subtracted from the number of the peaks and the last peak. Equivalent to. And the last annotation: In fact, people are close to the goal, which people pass in front of the labyrinth or do not choose randomly, and the number of other methods used by people when trying to get out of the labyrinth is the same. Walter D. Pulhen, who created a great program to create a Daedalos labyrinth, has a huge list of the moment it makes the labyrinth difficult. (Many of these moments can be realized by adding rudimentary weight to the equation. 1 and 2 above) What kind of statistics are the complicated ordinary puzzles using 3x4 sliding blocks? 2x8? 4x5? How much are the complex and difficult simple^3 puzzles standing from the most complex simple^3 SBP? Is it difficult to explore all ordinary SBPs with a volume of 4x4? Simple SBP? (Robert Smith) Is the binity of the SBP's bidgling meaningful? Why didn't anyone find the most difficult transaction of 15 puzzles in this way? (According to KARLEMO and OsterHord, only 1, 3 TBs that contain almost all huge outer discs are needed! It is necessary to recite and write strict disks in the crow. , In fact, it will be a certain amount slow.) (Or not?) Why 132? What are the very difficult puzzles of two simple slide blocks on a square grid? ZIEGLER-HUNTS & amp; amp; amp; ziegler-hunts sets the bottom of NXN, N & Amp; amp; GT grid 4N-16; it is not so difficult to place it, leaving a riddle for readers. 。 Is there the best difficulty than BB-Metrics? Is there the best way to find all kinds of puzzles from the sliding block? Is it possible to see that SBP was solved without sorting all possible positions? (This question is suggested in a notebook on the Martin Garden's sliding block puzzle published in the February 1964 issue of the Scientific American magazine.) (Robert Smith) How does the SBP conclusion change when you make atom arrangement in a puzzle? Is the 3D puzzle that slides the block interesting? Is it worth making these puzzles online base based on OEIS and Edward Hodan's "Puzzle using Gliding Block", which inherits the genealogy? DRIS DE CLERK, "PUZZLES with Glaid Blocks" http: // puzzless. Net/net/ Analog Bit's mysterious Tim, "Sliding Block Puzle Solver", http: // Analogbit. Com/Software/Pazletools Martin Gardner "Hypnotic Character of Block Puzzle" "Scientific American" 210: 122-130, 1964. L. E. HORDERN, "Sliding Block Puzzless", Oxford University Press, 1986. IVAN MOSKOVICH, "The Monty Hall Problem and Other Puzzless". Ruben Grönning Spaans, "Improving the Solving of Sliding Block Puzless with Reachoning at the Meta-Level," http: // daim. 5516. John Tromp and Rudy Cilibrasi, "The Limits of Complexity in Rush-Hour Logic," Arxiv. Org/PDF/CS/0502068 Think Nice & Amp; amp; Mark Engelberg, "THE INSIDE STORY on E/RUSHHOUR/CREATING2500CHALLENGES Is there any answer to questions or arguing data? Leave a comment or (rot13) to the author to GRPUVR314@tznvy. pbz. The reader of this blog may have noticed that I haven't updated it for the last four months. The purpose of this fil l-in article is to explain the reason. First, it's easy to blame the season. In the summer, it is known as the seasonal season, and forget about important things and read the web manga instead. You can also blame the wonderful 3D printers I purchased. The 3D printer quickly filled my desk and emptied dozens of small plastic models and puzzles from the wallet. It may look plausible, but I want to blame the "work" of the project I worked on, especially the sliding block puzzle. As you may know about a year ago, I am very interested in really difficult sliding block puzzles such as panx puzzles (30. 000 hands) and sunshine (729 hands). James Stevens of PUZZLEBEAST. com is a pioneer that made a highly difficult block puzzle using a computer. Using his PUZZLEBEAST program, we made at least 23 difficult sliding block puzzles from 18 to 148 hands! In addition, many of these puzzles are limited to several pieces, at least 11 puzzles, "Prime-Plain", that is, moving one piece to the corner! Even Simple City Puzzle uses only 4 pieces for 4x4 squares and only needs 18! Oscar Van Devente, the creator of many mechanical monsters, has developed a 3D print version of Simple City Puzzle, calling it the "most difficult sliding puzzle in 4x4 squares." Judging from Stevens' description of PuzzleBeast, PuzzleBeast uses a genetic algorithm to create puzzles. It starts with a random set of puzzles, as far as I can tell. It picks the hardest puzzle, and in the next generation it randomly "mutates" the best puzzle from the previous generation, for example by adding elements, moving elements, changing elements, deleting elements, etc. It repeats this process over and over, and eventually ends up with a complex puzzle with sliding blocks. It seemed to work very well for him, so he ended up trying to make his own sliding block evolver puzzle. The SBP project started like this: The earliest version of my SBP-evolver was written in a Mathematica system and was very manual. First, I randomly generated five 4x5 rectangular puzzles with no constraints on the number of shapes, interpreted each puzzle as a "simple puzzle made of sliding blocks" (see Napal 1), and loaded it into Analogbit's online puzzle resolver from sliding blocks. Next, we took the best two puzzles, converted them to a one-dimensional array, "alternated" them, and randomly mutated the squares (i. e. each square had roughly a 1/5 chance of being added or subtracted by 1). This may not be very obvious, so here's an example: If the best two puzzles from the previous generation were 0. 19, 1, 2 0. 19, 0, 3 2, 1, 1, 1, 1 2. 19, 1, 1, 1 0, 2, 0, 0, 0, 2 and 1, 3, 2, 0 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1 0, 1, 19, 2 The "alternations" would then look like this: 0, 19, 1, 3, 2, 19, 1, 1, 0, 3, 0, 0, 1, 1, 0, 0, 1, 1, 0, 2 Then, from among them, a "mutant" emerges and the cycle repeats. Note: 1. "Simple block puzzle" is my personal term based on the definition of Nick Baxter on the sliding block puzzle page. For me, each small thing is distinguished only by its own form, and the task is to transfer the small left end to the smaller one on the lower right. The original definition is somewhat ambiguous, but in effect, if there is no piece in the upper left square, it is not a true ordinary block puzzle. Except for this, almost all of the puzzles recorded in this first volume have been copied directly from the Mathematica system notebook, and as a result, appropriate analysis of the quantity is clearly lacking. The analysis of the solution is easy: If the parts with two numbers are the same number, and if they are orthodox, both belong to the same parts. Otherwise, they belong to different parts. (Eventually, a parser was created, for example, so that these puzzles meet the standards, for example, to make it easier to recite.) Eventually, steps and moves are different luggage. This is because in one case, the piece moves to one box, and in another case it moves to an arbitrary number of boxes. Edward Hodann's book "Sliding Piece Puzzless" has completely elucidated this issue. In the first version of SBP Evolber, surprising results were obtained! From 4 to 10, about 10 generations, from four unpopular puzzles and one 8-step puzzle (one of which is 58 steps) It has evolved to! Of course, this is not a big result, as these puzzles require 121 steps, like Bob Henderson and Gil Dogon's "Quzzle-Killer". For example, this early experience was only a concept proof. In the end, I got tired of making these puzzles using Analogbit and decided to write a program in C#. Apart from that, the population will increase significantly (probably 100 or its range), and the number of generations will increase significantly. I wrote the code to handle the puzzle for Jimslide, processed the obtained results, and finally moved after a while! Almost immediately, it was launched with a large amount of 4x5 puzzles (10 million questions) and processed overnight. Actually it took about four days, but the best one was 176 hands puzzles! 176 Puzzle (not the best among simple puzzles) SBP Evolver also showed a typical behavior of most of the worse genetic evolution programs where I wanted. For a while, the program found a really good optimization and had a small optimization that would make the puzzle better, and stuck to a specific puzzle for a while. Even if it was due to a pure coincidence that had no specific puzzle in the generation of questions. So it may not be enough to find the best puzzle in four days. Apart from that, Bob Henderson's Gauntlet #2 is also a normal block puzzle, but it has exceeded 176 puzzles with 235 hands! As far as his explanation on Andrea Gilbert's CLICKMAZES site, Bob Henderson is making sliding blocks in a completely different way. He enters a series of pieces and creates all possible ways in which his packaging program is placed in sliding puzzles. And put it on your sliding puzzle program. In fact, I think this will get results much faster. After thinking, I decided to solve the usual 4x4 puzzle. This time, a simple puzzle of 125 hands was completed in about a day! However, it turned out that this puzzle could make 132 hands puzzles. Interestingly, when I did the same calculation again, I got a child and 132! By the way, of course, there was a question that this puzzle is the best of a simple 4x4 puzzle. Red is the bottom fair. This problem can be easily solved by simply generating all 4x4 possible positions, interpreting simple SBP, and setting one of them. But how do you set the first one? After all, 4x4 has 16 possible block types (including holes), and each space may be one of 16, so it is 16^16 = 18. 446. 744. 073. 709. 551. 616 combinations are possible! I decided to use four colors of worship. 0 was used for holes and 1, 2, and 3 were used for other colors. After coloring the board in four colors, the parser assigned the original number to all blocks and deleted all the duplicate ones (in fact, this was wrong: holes may be different, and as a result, four colors. As a result, it happened to be applied to the block. In about a day, the puzzle intelligence processed 4294967296 boards and returned a total of 52. 825. 604 boards! Similarly, the other two methods that may work even better are generated from one component, and then two parts from the combination of all no n-reflected substrates from one part. It is a method to generate all boards from. There is also a method based on the dynamic planning law I am currently using, which is included in the Sbpfinder source code in the section below this article (although it is too long to write here). After dividing the 52 825 604 types of boards into files according to the number of components, the host software loaded each file to the hash table and solved the first puzzle. After solving the puzzle, the software processed the result and deleted the puzzle described in the hash table decision. Then decide the new first puzzle. This algorithm is not very fast (it took 48 days), but there are at least one advantage: by dividing the puzzle into a file marked by the number of pieces, the number of A 4 × 4 MESH 4 pieces of A 4 × 4 Mesh 4 You can return the most complicated puzzle! The table below shows the simplest puzzle of 4x4 squares from 2 pieces to 15 pieces. Due to the millions of questions during the calculation, all the following puzzles are unpolished, and are very suspicious. In addition, SBP is determined which figure is on the top and the line behind the shape, so there are only simple SBPs in the following puzzles, only simple SBP. The one has been deleted. (Confused? Http: // www. Johnrausch. COM/Slidblockpazles/4 × 5. Check HTM) First, the result was not obviously strict because both the task of the task and the converter of the Jimslides puzzle were found. Furthermore, SBP-EVOLVER (JimslideS's puzzle converter and search engine are also controlled), consider each puzzle as a simple one, select the specified figure, and pass the line behind the line on the board. Was developed. Finally, there are mysterious phenomena related to 12 shapes. Decompose 1x2 into two parts 1x1 and shuffle the remaining parts to get 9 more hands! Since then, after I have created a 4x4 calculation, especially another program to replenish the entire search process, I will return the best results, and to check if these results match. There is. You need to be several times faster. The optimization that I am working on includes the following: I use the first of other methods to fin d-sbp's possibility of puzzles more quickly, -A "I have solved" only "puzzles, that is, the motivated numbers are already at the bottom right, only the puzzle that can be moved from the current position. (This is based on the idea of John Trump and Rudy Chili Brush, c o-authored Hour of the Pick or Difficalty). In fact, about 1/4 of the 4x4 SBP position is the fact that the decision is located in the upper right corner in most positions, and in fact, quite a lot of elementary, rudimentary. It turned out that the only true limit was made by the fact that it is essential to own an opportunity to move). -(This is a possibility that the search is performed with two diagnoses, and once for sock quests, only the actual puzzles in the group are elsewhere, otherwise, all the actual actual. I will search for a further starting position from the position, which is about 3 slower than Jimslide, but the puzzle solved puzzle is solved. It will be compensated for the fact that it may be a distant number from the lis t-some of the 14 or more! However, he means that he has no opportunity to grasp the puzzle, and my actions have started gypsiga! The preparatory research program has actually established a decision to actually observe the news, for example, the expected work time in the day and night! Anyway, this is my observation, what happened, and I apologize for my conditional silence. This is the sixth post from a gathering of Gardner (final): 1 2 3 4 5 5 5 The last day of the meeting for Gardner 9 began with such a slow morning call. < SPAN> -Sbp is the first to find the puzzle with a high possibility of SBP, the first of other methods, -A "I have solved" only "puzzles, that is, the motivated numbers are already at the bottom right, only the puzzle that can be moved from the current position. (This is based on the idea of John Trump and Rudy Chili Brush, c o-authored Hour of the Pick or Difficalty). In fact, about 1/4 of the 4x4 SBP position is the fact that the decision is located in the upper right corner in most positions, and in fact, quite a lot of elementary, rudimentary. It turned out that the only true limit was made by the fact that it is essential to own an opportunity to move). -(This is a possibility that the search is performed with two diagnoses, and once for sock quests, only the actual puzzles in the group are elsewhere, otherwise, all the actual actual. I will search for a further starting position from the position, which is about 3 slower than Jimslide, but the puzzle solved puzzle is solved. It will be compensated for the fact that it may be a distant number from the lis t-some of the 14 or more! However, he means that he has no opportunity to grasp the puzzle, and my actions have started gypsiga! The preparatory research program has actually established a decision to actually observe the news, for example, the expected work time in the day and night! Anyway, this is my observation, what happened, and I apologize for my conditional silence. This is the sixth post from a gathering of Gardner (final): 1 2 3 4 5 5 5 The last day of the meeting for Gardner 9 began with such a slow morning call. I use the first of other methods to fin d-sbp's possibility of puzzles more quickly, -A "I have solved" only "puzzles, that is, the motivated numbers are already at the bottom right, only the puzzle that can be moved from the current position. (This is based on the idea of John Trump and Rudy Chili Brush, c o-authored Hour of the Pick or Difficalty). In fact, about 1/4 of the 4x4 SBP position is the fact that the decision is located in the upper right corner in most positions, and in fact, quite a lot of elementary, rudimentary. It turned out that the only true limit was made by the fact that it is essential to own an opportunity to move). -(This is a possibility that the search is performed with two diagnoses, and once for sock quests, only the actual puzzles in the group are elsewhere, otherwise, all the actual actual. I will search for a further starting position from the position, which is about 3 slower than Jimslide, but the puzzle solved puzzle is solved. It will be compensated for the fact that it may be a distant number from the lis t-some of the 14 or more! However, he means that he has no opportunity to grasp the puzzle, and my actions have started gypsiga! The preparatory research program has actually established a decision to actually observe the news, for example, the expected work time in the day and night! Anyway, this is my observation, what happened, and I apologize for my conditional silence. This is the sixth post from a gathering of Gardner (final): 1 2 3 4 5 5 5 The last day of the meeting for Gardner 9 began with such a slow morning call. As a result, I missed the first report and went to the conference room during the second report on Karl Chafer about Dancing Tessel. It was mainly composed of several videos, and a regular dance was projected along a shaft, and a video test was performed. Next, it was a short report on expanding the sidelor long (SAS) similar orthodox system for thre e-dimensional shapes using as small as possible. One of the most interesting reports in the first session was Linda Zai a-Palmer Linda's report, why the infinite number is 0. 999999 ... Immediately after that, there was a report on a puzzle that searched for a specific phrase from the picture of Salvador Dali. Dali's puzzle was very simple. But what I particularly liked was a bullcard polster's technique that balances laptops on a bedside table. He shows how to start with a simple disassembly by Martin Gardner, develop it, and remain a place to put laptops in a wel l-balanced manner, so that there are places to place other things on a puzzle or bedside table. Ta. During the break, my mother and I went to the exhibition hall where participants exhibited. Most of the exhibits were already over, but some were first unveiled. One of them was a mysterious and diverse sculpture exhibition venue using cardboard eggs for eggs, and my mother was able to talk to Ginny Mozuri, who made it. She received a model of the eigh t-sided body and a slightly unusual way to make it. After the break, it was a story of a thre e-dimensional packing puzzle that attached different spheres with adhesive to create a polyomi n-like shape. Because the details are spherical, some puzzles need to stick a police officer with "clicking", but that is usually the case. In this session, we talked about the best demonstration of the ED PEGG about the WolFram demonstration project, for example, a program to find the smallest box that fits in a 1/n square. For example, a program that finds the smallest box that fits in a 1/n square, and how to solve the planting problem of the orchard. < SPAN> As a result, I missed the first report completely and went to the conference room during the second report on Karl Shafer's Dancing Tessel. It was mainly composed of several videos, and a regular dance was projected along a shaft, and a video test was performed. Next, it was a short report on extending the side call long (SAS) similar theorem for thre e-dimensional shapes using as small as possible. One of the most interesting reports in the first session was Linda Zai a-Palmer Linda's report, why the infinite number is 0. 999999 ... Immediately after that, there was a report on a puzzle that searched for a specific phrase from the picture of Salvador Dali. Dali's puzzle was very simple. But what I particularly liked was a bullcard polster's technique that balances laptops on a bedside table. He shows how to start with a simple disassembly by Martin Gardner, develop it, and remain a place to put laptops in a wel l-balanced manner, so that there are places to place other things on a puzzle or bedside table. Ta. During the break, my mother and I went to the exhibition hall where participants exhibited. Most of the exhibits were already over, but some were first unveiled. One of them was a mysterious and diverse sculpture exhibition venue using cardboard eggs for eggs, and my mother was able to talk to Ginny Mozuri, who made it. She received a model of the eigh t-sided body and a slightly unusual way to make it. After the break, it was a story of a thre e-dimensional packing puzzle that attached different spheres with adhesive to create a polyomi n-like shape. Because the details are spherical, some puzzles need to stick a police officer with "clicking", but that is usually the case. In this session, we talked about the best demonstration of the ED PEGG about the WolFram demonstration project, for example, a program to find the smallest box that fits in a 1/n square. For example, a program that finds the smallest box that fits in a 1/n square, and how to solve the planting problem of the orchard. As a result, I missed the first report and went to the conference room during the second report on Karl Chafer about Dancing Tessel. It was mainly composed of several videos, and a regular dance was projected along a shaft, and a video test was performed. Next, it was a short report on expanding the sidelor long (SAS) similar orthodox system for thre e-dimensional shapes using as small as possible. One of the most interesting reports in the first session was Linda Zai a-Palmer Linda's report, why the infinite number is 0. 999999 ... Immediately after that, there was a report on a puzzle that searched for a specific phrase from the picture of Salvador Dali. Dali's puzzle was very simple. But what I particularly liked was a bullcard polster's technique that balances laptops on a bedside table. He shows how to start with a simple disassembly by Martin Gardner, develop it, and remain a place to put laptops in a wel l-balanced manner, so that there are places to place other things on a puzzle or bedside table. Ta. During the break, my mother and I went to the exhibition hall where participants exhibited. Most of the exhibits were already over, but some were first unveiled. One of them was a mysterious and diverse sculpture exhibition venue using cardboard eggs for eggs, and my mother was able to talk to Ginny Mozuri, who made it. She received a model of the eigh t-sided body and a slightly unusual way to make it. After the break, it was a story of a thre e-dimensional packing puzzle that attached different spheres with adhesive to create a polyomi n-like shape. Because the details are spherical, some puzzles need to stick a police officer with "clicking", but that is usually the case. In this session, we talked about the best demonstration of the ED PEGG about the WolFram demonstration project, for example, a program to find the smallest box that fits in a 1/n square. For example, a program that finds the smallest box that fits in a 1/n square, and how to solve the planting problem of the orchard. The report following Ed Peg's performance was one of the most expected of the tournament. It was to search for one figure that covers the entire plane, which was an unresolved problem, asynchronously. Joshua Socler succeeded in finding one hexagonal tiles (although there are selection rules), and assembling it will be similar to the laying of Selpinski. He also made a thre e-dimensional tile that works in the same way. When a music box is played, another music box is played a few seconds later. After the performance of the VI cart, the lunch break started, but I went straight to the gift exchange corner instead of eating lunch, protected the rows to get the gift from almost everyone, and received the present as well. Repeated. Apparently, everyone decided to line up early. I was behind Bram Cohen, the inventor of Bittorrent. Many supe r-complicated puzzles have a great idea hidden. While waiting, he came out of a few but complex puzzles, and one of them was almost unraveled. Another cast marble could not be solved immediately, but it may have been a little more. Immediately, I lined up in the row of receiving the present and received a huge package (I finally carried it). In addition, the people on the next table have expanded a large thre e-dimensional, for example, a wooden item that looks like a gear, and the 59th constellation of the huge positive 20 body seen on the third day. I received some different objects, including some photos of Kaspar Schwabe. The report following the < Span> Ed Peg's performance was one of the most expectations in the tournament. It was to search for one figure that covers the entire plane, which was an unresolved problem, asynchronously. Joshua Socler succeeded in finding one hexagonal tiles (although there are selection rules), and assembling it will be similar to the laying of Selpinski. He also made a thre e-dimensional tile that works in the same way. When a music box is played, another music box is played a few seconds later. After the performance of the VI cart, the lunch break started, but I went straight to the gift exchange corner instead of eating lunch, protected the rows to get the gift from almost everyone, and received the present as well. Repeated. Apparently, everyone decided to line up early. I was behind Bram Cohen, the inventor of Bittorrent. Many supe r-complicated puzzles have a great idea hidden. While waiting, he came out of a few but complex puzzles, and one of them was almost unraveled. Another cast marble could not be solved immediately, but it may have been a little more. Immediately, I lined up in the row of receiving the present and received a huge package (I finally carried it). In addition, the people on the next table have expanded a large thre e-dimensional, for example, a wooden item that looks like a gear, and the 59th constellation of the huge positive 20 body seen on the third day. I received some different objects, including some photos of Kaspar Schwabe. The report following Ed Peg's performance was one of the most expected of the tournament. It was to search for one figure that covers the entire plane, which was an unresolved problem. Joshua Socler succeeded in finding one hexagonal tiles (although there are selection rules), and assembling it will be similar to the laying of Selpinski. He also made a thre e-dimensional tile that works in the same way. When a music box is played, another music box is played a few seconds later. After the performance of the VI cart, the lunch break started, but I went straight to the gift exchange corner instead of eating lunch, protected the rows to get the gift from almost everyone, and received the present as well. Repeated. Apparently, everyone decided to line up early. I was behind Bram Cohen, the inventor of Bittorrent. Many supe r-complicated puzzles have a great idea hidden. While waiting, he came out of a few but complex puzzles, and one of them was almost unraveled. Another cast marble could not be solved immediately, but it may have been a little more. Immediately, I lined up in the row of receiving the present and received a huge package (I finally carried it). In addition, the people on the next table have expanded a large thre e-dimensional, for example, a wooden item that looks like a gear, and the 59th constellation of the huge positive 20 body seen on the third day. I received some different objects, including some photos of Kaspar Schwabe. In order to discover it, I brought a large gift in the hotel room, but although the weight of the wrap was reflected in the inside, the mood when opened was just Christmas. Ta. Digital photos of mathematics cubes with only 9 numbers on the side, plastic ring sets that can be exchanged for designs based on trade travelers, CDs of quite high quality paintings and G4G8 replacement books. , Puzzle's Peace Set and Hammer can open the door with the support of a hammer, books about mathematical formulas that have changed the world, two books, "A New Kind of Science" (and gravity is born from here, etc.). Back scrapers and cranes. These are only a small part of the bag, and it is clear that this blog will be very long if you enumerate. When I reached the bottom of the bag, session 3 had already begun. I happened to run downstairs to see the Gordon Hamilton report (from the magical mathematics museum) and saw how ope n-end problems were taught in kindergarten to high school. This is similar to the problem of packing the circle (which small square can be packed with N circles), and the speculation 3N+1 (a colatz sequence is all 4, 2, 1). In the same session, Solomon Gorom talked about this pentamino game on the NXN board. Pento Mino Game is a very interesting tw o-player game that puts pentimino alternately on 8x8 boards. Players who can't put the piece first lose. The most attractive in this session was the Fun with Cardboard Eggs by Ginnie Mosley. She talked about how many platonic stiff body was made in cardboard egg packs! It's a very simple thing that just mixes stri p-shaped things at the top of the cardboard box and arranges the ribs, but its work is also attractive. Immediately after that, a report on the restoration of all kinds of old text adventures, which has nothing to do with mathematics (still as cool). The report created by Adam Atkinson was to cross compile old text adventures (operations on the main frame) so that they could play on recent computers. Almost all of them are archived in IFARCHIVE. ORG (interactive fiction archive), and covers Acheton, probably the third text adventure in history. Don't be eaten by GRUE. After a short break, the G4G9 last session started. After Kate Jones talked about Pento Mino Puzzle, Bill Marins wrote Martin Gardner, who wrote EXPERT ATTHE CARD TABLE, the most important book for hand dexterity using Trump. I searched and wrote his name as "S. W. ERDNASE". You can twist this to E. S. Andtrews, but that makes everything more complicated. To date, there are five suspects, two Gardner, and three others have been found, but the author remains hidden. Subsequently, Ibasawa Hirokazu (commonly known as Ibahiro) talked about how to solve the subclass of "Hut Team Puzzle" and other variations in this issue. Shortly later, Colin Wright said, "How far is the moon? And about the juggling notation. The first report remained behind the scenes (here is the PDF), but the story of the juggling was wonderful. He scored five goals. In addition to juggling, it shows how to think of its own tricks using the notation, and some of them are insanely complicated, and some are trivial. It has some reductions of the versatile color, so it should be hanging from the ceiling of the attrium. I made the last report. After the last call and words, G4G9 was over. But (at least for me) the pleasure continued. Dick Estherle invited me to a dinner at Varsity JR, an old snack that has been operating for 45 years (along with Bill Gosper, MOM, Julian, Corey Hunts). Bill and Julian declined, but the rest went. < SPAN> After a short break, the G4G9 last session started. After Kate Jones talked about Pento Mino Puzzle, Bill Marins wrote Martin Gardner, who wrote EXPERT ATTHE CARD TABLE, the most important book for hand dexterity using Trump. He searched and wrote his name as "S. W. ERDNASE". You can twist this to E. S. Andtrews, but that makes everything more complicated. To date, there are five suspects, two Gardner, and three others have been found, but the author remains hidden. Subsequently, Ibasawa Hirokazu (commonly known as Ibahiro) talked about how to solve the subclass of "Hut Team Puzzle" and other variations in this issue. Shortly later, Colin Wright said, "How far is the moon? And about the juggling notation. The first report remained behind the scenes (here is the PDF), but the story of the juggling was wonderful. He scored five goals. In addition to juggling, it shows how to think of its own tricks using the notation, and some of them are insanely complicated, and some are trivial. It has some reductions of the versatile color, so it should be hanging from the ceiling of the attrium. I made the last report. After the last call and words, G4G9 was over. But (at least for me) the pleasure continued. Dick Estherle invited me to a dinner at Varsity JR, an old snack that has been operating for 45 years (with Bill Gosper, MOM, Julian, Corey Hunts). Bill and Julian declined, but the rest went. After a short break, the G4G9 last session started. After Kate Jones talked about Pento Mino Puzzle, Bill Marins wrote Martin Gardner, who wrote EXPERT ATTHE CARD TABLE, the most important book for hand dexterity using Trump. He searched and wrote his name as "S. W. ERDNASE". You can twist this to E. S. Andtrews, but then everything becomes more complicated. To date, there are five suspects, two Gardner, and three others have been found, but the author remains hidden. Subsequently, Ibasawa Hirokazu (commonly known as Ibahiro) talked about how to solve the subclass of "Hut Team Puzzle" and other variations in this issue. Shortly later, Colin Wright said, "How far is the moon? And about the juggling notation. The first report remained behind the scenes (here is the PDF), but the story of the juggling was wonderful. He scored five goals. In addition to juggling, it shows how to think of its own tricks using the notation, and some of them are insanely complicated, and some are trivial. It has some reductions of the versatile color, so it should be hanging from the ceiling of the attrium. I made the last report. After the last call and words, G4G9 was over. But (at least for me) the pleasure continued. Dick Estherle invited me to a dinner at Varsity JR, an old snack that has been operating for 45 years (with Bill Gosper, MOM, Julian, Corey Hunts). Bill and Julian declined, but the rest went. Dinner was delicious (especially the burgers) and conversation with Oesterle was very enjoyable. I had brought along a puzzle (the same one from the prelude) along with the box, and he was able to solve it in record time by simply shaking it vigorously. He also showed me two versions of the same puzzle using available materials. First, place three cups in an equilateral triangle so that the blades of each cup can reach each other. Second, use a knife to place the salt shaker in the center of the triangle on the table. (Then we put the cup down so the knife can't reach it, and balance the salt shaker on the three knives again. Corey and I ended up solving this problem by making straw decorations (my conclusion is that it's hard to slide the knife through the straw and only use two knives). To avoid spoilers, it's here: http://daftmusings. stattenfield. org/wp-content/uploads/2010/04/Neil-and-Corey-at-the-Varsity-copy. jpg. After dinner, Dick Oesterle drove us back to the Ritz Carlton, and we went back to our rooms and played puzzles until bedtime. The next day, I got up pretty early to pack for the trip back to San Jose. I met Bill Gosper in the hotel lobby and we took a cab to the airport. On the flight back (with an exchange to Chicago), I reviewed all the exchange gifts in my bag while Bill Gosper programmed his laptop. As a result, due to the time difference, we had breakfast for 2 hours. After getting my degree, we flew down to San Jose, went to my house, and then Bill went back to his house. And because of the time difference, we ended up playing puzzles for the rest of the day. And so ended our epic meeting at Gardner 9. It was truly amazing skill from start to finish, and I met so many new people and discovered so many puzzles, magic tricks, and optical illusions. I'll definitely go back again, next time and beyond. It's definitely one of the best events I've ever attended. As an epilogue, Martin Gardner passed away on May 22nd. This news was unimaginably sad and sudden for me. He was one of the most important people who ever lived, both for mathematics and for many other disciplines. He definitely helped popularize M. K. Escher, Godel, Escher, and Bach, and introduced arithmetic in an interesting way to at least all members of G4G. He was a really unusual person. This is the fifth article of a series of articles on preparation for Gardner: 1 2 3 4 The next day, when I woke up, the first report had already begun. Fortunately, the meeting was held at the hotel where I was staying, so I arrived just a few minutes later. Jean Pedelsen first spoke and talked about the vast spread of all kinds of polyhedron. Zudrafco Givcovich has announced a puzzle called "Memoriq". For example, it is not easy to actually make a square. Al Skel gave a lecture on the theme of "the essence of beliefs", and talked about the illusion of various controversy that would change when a simple line was added, and the upsid e-down musical number that can be heard at first. 。 There was also a story about a musical number that turned upside down. Greg Federixon reported on "Symmetric ant i-economy in square and cubes." He has shown a lot of examples of a large amount of squares and cubes in large quantities, using a fairly symmetrical method to the smallest square or cube. He also recommended examples of splitting with hinges, some of which were appropriate. < SPAN> This is the fifth article of a series of articles on preparation for Gardner: 1 2 3 4 The next day, when I woke up, the first report had already begun. Fortunately, the meeting was held at the hotel where I was staying, so I arrived just a few minutes later. Jean Pedelsen first spoke and talked about the vast spread of all kinds of polyhedron. Zudrafco Givcovich has announced a puzzle called "Memoriq". For example, it is not easy to actually make a square. Al Skel gave a lecture on the theme of "the essence of beliefs", and talked about the illusion of various controversy that would change when a simple line was added, and the upsid e-down musical number that can be heard at first. 。 There was also a story about a musical number that turned upside down. Greg Federixon reported on "Symmetric ant i-economy in square and cubes." He has shown a lot of examples of a large amount of squares and cubes in large quantities, using a fairly symmetrical method to the smallest square or cube. He also recommended examples of splitting with hinges, some of which were appropriate. This is the fifth article of a series of articles on preparation for Gardner: 1 2 3 4 The next day, when I woke up, the first report had already begun. Fortunately, the meeting was held at the hotel where I was staying, so I arrived just a few minutes later. Jean Pedelsen first spoke and talked about the vast spread of all kinds of polyhedron. Zudrafco Givcovich has announced a puzzle called "Memoriq". For example, it is not easy to actually make a square. Al Skel gave a lecture on the theme of "the essence of beliefs", and talked about the illusion of various controversy that would change when a simple line was added, and the upsid e-down musical number that can be heard at first. 。 There was also a story about a musical number that turned upside down. Greg Federixon reported on "symmetry ant i-economy in squares and cubes." He has shown a lot of examples of a large amount of squares and cubes in large quantities, using a fairly symmetrical method to the smallest square or cube. He also recommended examples of splitting with hinges, some of which were appropriate. After a short break, the second session started. Pavloss Holman made a wonderful report, "Hacker and Invention." Introducing a method of irradiating a mosquito by irradiating a mosquito, changing the voice of the voice mail of Al Skkel's mobile phone with his personal number, recommending a bot that approaches by car and teaches passwords. He advised how to quickly break the lock using a ratfill and a hammer. After this lecture, I joined Bill Gossper. He was planning to demonstrate the Game of Life computer set up to John Conway to calculate the pi. For example, how about a universal computer that calculates the number of the golden ratio, and how to proceed to a specific step in life simulation in the Python script, not a normal way to simulate the model in Google-1 step. Like. For this reason, I was a little delayed from the final report of the day, that is, the mathematical image educational program created at the Tom Roger's house (from the knot to the big zonoid pavilion). I finished lunch quickly (that is, without eating anything) and got on the bus. On the way, I tried difficult questions that had no manuals and talked to other members. When we arrived, many Japanese dinner was lined up on the table, so we ate it, and then built various images and saw what was already installed. The most attractive was the sculptures of the iron polyhedron created by George Heart, the incredible boxes that could stand inside, and the big and dark sculptures that stood on all others. 。 After lunch, I was able to help the base of Zonohedoral Pavilion. At the end of this, I went to the rooftop of the pavilion, and advised other participants on many puzzles, including versions of Enigma Puzzle and "sticks" puzzles using the remaining sticks later. < SPAN> After a short break, the second session started. Pavloss Holman made a wonderful report, "Hacker and Invention." Introducing a method of irradiating mosquitoes by irradiating mosquitoes, changing the voice of Al Skkel's mobile phone with his personal number, recommending a bot that approaches by car and teaches passwords. He advised how to quickly break the lock using a ratfill and a hammer. After this lecture, I joined Bill Gossper. He was planning to demonstrate the Game of Life computer set up to John Conway to calculate the pi. For example, how about a universal computer that calculates the number of the golden ratio, or not a normal way to simulate the model in Google-1 step, but to go to a specific step in life simulation in the Python script. Like. For this reason, I was a little delayed from the final report of the day, that is, the mathematical image educational program created at the Tom Roger's house (from the knot to the big zonoid pavilion). I finished lunch quickly (that is, without eating anything) and got on the bus. On the way, I tried difficult questions that had no manuals and talked to other members. When we arrived, many Japanese dinner was lined up on the table, so we ate it, and then built various images and saw what was already installed. The most attractive was the sculptures of the iron polyhedron created by George Heart, the incredible boxes that could stand inside, and the big and dark sculptures that stood on all others. 。 After lunch, I was able to help the base of Zonohedoral Pavilion. At the end of this, I went to the rooftop of the pavilion, and advised other participants on many puzzles, including versions of Enigma Puzzle and "sticks" puzzles using the remaining sticks later. After a short break, the second session started. Pavloss Holman made a wonderful report, "Hacker and Invention." Introducing a method of irradiating a mosquito by irradiating a mosquito, changing the voice of the voice mail of Al Skkel's mobile phone with his personal number, recommending a bot that approaches by car and teaches passwords. He advised how to quickly break the lock using a ratfill and a hammer. After this lecture, I joined Bill Gossper. He was planning to demonstrate the Game of Life computer set up to John Conway to calculate the pi. For example, how about a universal computer that calculates the number of the golden ratio, and how to proceed to a specific step in life simulation in the Python script, not a normal way to simulate the model in Google-1 step. Like. For this reason, I was a little delayed from the final report of the day, that is, the mathematical image educational program created at the Tom Roger's house (from the knot to the big zonoid pavilion). I finished lunch quickly (that is, without eating anything) and got on the bus. On the way, I tried difficult questions that had no manuals and talked to other members. When we arrived, many Japanese dinner was lined up on the table, so we ate it, and then built various images and saw what was already installed. The most attractive was the sculptures of the iron polyhedron created by George Heart, the incredible boxes that could stand inside, and the big and dark sculptures that stood on all others. 。 Meanwhile, the production of the Universal Ball was getting out of hand: Back in the main area, many sculptures were already finished, such as the Chinese knot and George Hart's sculpture. I talked with Clifford Pikova about various things, such as the non-paradox that 9 is in 100% of all integers, and about some illustrations for Pikova's new book Mathematics. I also talked with Ivan Moscovic, who was nearby, about various puzzles, such as his mirror sliding block puzzle series. Soon, almost all the sculptures were finished, except for the pavilion, which was almost finished, and it was already dark. We had a decent dinner, but the tables were taken and I happened to sit near where Gosper was. We talked for a while and told him about the formula for finding pi to 42 billion digits, which quickly fell apart. After dinner, we went to Tom's house. As I said, Tom's house had a lot of puzzles. I played with a few puzzles, including a Bali puzzle in three parts and a Japanese puzzle, but I came across one that fell apart and I couldn't put it back together. By that time, it was time to go back to the hotel. I ended up sitting next to George Hart and the people who took photos at Tom's house that day at the bus stop in the back, and we chatted the whole time. It was a great day. Only one more day left until the conference is over. This is the fourth in a series of blog posts about the Gathering For Gardner 9:1 2 3 conference. I was in about the fifth space, but most of the members decided not to take off, so I borrowed the second space and performed for 20 seconds. Of course, this was unexpected, and I ended up with 30 seconds to think about what to say. When my time came, I managed to give an overview of my personal website, this blog, and my own scratch project in less than the allotted 20 seconds. Most of the others gave short explanations of what they did, some of them over a minute, but Ed's concert still didn't fit into the allotted 15 minutes.
Metrics
a.k.a. redefining the problem
The BB Metric
a.k.a. attempting not to invoke the xkcd reference
Open Problems
a.k.a. things for an idling programmer to do
Sources
What I’ve Been Working on Lately
You need to pay attention to several points (and give up your responsibilities): First, the actual graph of which position can reach each other with one action depends on the type of stroke. -Metric is a six competitors that do not actually solve the problem! Second, it is very difficult to solve the problem of calculating the average route length between the two columns. In particular, in the algorithm, which gives the maximum route length between the two points in a multiple time, it is possible to check whether the number of Hamilton has a route exceeding the percentage time. Since the Hamilton route problem is NP-FULL, the problem of the seller, the problem of the bag, and the color of the count can be solved. At mult i-section time! Finally, I have not yet confirmed this statistics in the actual puzzle, and no one has come up with the same complex statistics. If anyone knows, please let me know!
G4G9, Day 5: Balancing Laptops, Mobius Music, and Egg Cartons
G4G9, Day 4: Lasers, Sculptures, and Balloon Polyhedra
G4G9, Day 3: Random(Blog), Crazy Detectives, and the Rubik’s Cube
Gathering For Gardner, Day 2: Fractals, Puzzles, and Magic
G4G9, Day 1: Pencils, Optical Illusions, and Bar Bets
Gathering For Gardner 9: Prelude
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3 Clown Monty Letöltés Ingyen
A kaszinók varázslatos világa: a játék és az élet izgalmai
3 clown monty letöltés ingyen
A kaszinó és a turizmus: egy befektetési lehetőség
Mr Puzzles' Lowest Point is the thirty-sixth episode of Season 14 and the nine hundred and first overall to be uploaded on the SMG4 channel. The balloons in the monty golf hole- its actually the same number of digits as the code baby gives you in sister location. Modern Monty's Ocean "Take Me With You" Puzzle is a stunning 36 piece jigsaw puzzle, packaged in the sweetest mini suitcase with a durable metal handle and.
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