magicsquare6
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| magicsquare6 [2024/06/19 09:42] – [Storategies and Codes] mino | magicsquare6 [2025/08/15 14:08] (current) – [The number of magic squares of order six counted up to rotations and reflections] mino | ||
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| + | __[[magicsquare6-j|Move to the Japanese page]]__ | ||
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| ===== The number of magic squares of order six counted up to rotations and reflections ===== | ===== The number of magic squares of order six counted up to rotations and reflections ===== | ||
| <file - nms6.txt> | <file - nms6.txt> | ||
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| </ | </ | ||
| - | This number has been confirmed by completing the enumeration twice using hundreds of GPUs at cloud resource rental services. Though the number and models of GPUs used varied over time, the initial enumeration took about 80,000 hours of GeForce RTX-4090 and the second enumeration with an improved code took about 54,000 hours. | + | [[https:// |
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| + | This number has been confirmed by completing the enumeration twice using hundreds of GPUs provided | ||
| As the result of the second enumeration, | As the result of the second enumeration, | ||
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| ===== Correction history ===== | ===== Correction history ===== | ||
| - | More than thousand of instances of GPU server were used in the enumeration and some of them were unfortunately faulty and produced wrong results. To find and correct such errors, every subtotal was calculated at least twice and extra counting was done to determine the correct answer when a mismatch happened. There were following two cases where the initial result was incorrect. | + | More than a thousand of instances of GPU server were used in the enumeration and some of them were unfortunately faulty and produced wrong results. To find and correct such errors, every subtotal was calculated at least twice and extra counting was done to determine the correct answer when a mismatch happened. There were following two cases where the initial result was incorrect. |
| ==== corrected on 2023.09.07 ==== | ==== corrected on 2023.09.07 ==== | ||
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| * [[https:// | * [[https:// | ||
| * (18 of sub-subtoals are known to be incorrect, but are kept uncorrected intentionally.) | * (18 of sub-subtoals are known to be incorrect, but are kept uncorrected intentionally.) | ||
| - | | + | |
| [[strategies|Strategies in counting magic squares]] | [[strategies|Strategies in counting magic squares]] | ||
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| * Counts magic squares of an order from 3 to 6 up to [[https:// | * Counts magic squares of an order from 3 to 6 up to [[https:// | ||
| - | * Runs at a typical speed of 3.8G counts/sec on Nvidia GeForce RTX-4090 for order 6. | + | * Runs at a typical speed of 3.8G counts/ |
| * Nvidia GPU of Pascal architecture (sm_60) or newer is assumed. | * Nvidia GPU of Pascal architecture (sm_60) or newer is assumed. | ||
| * Multi GPU systems are supported. **[[https:// | * Multi GPU systems are supported. **[[https:// | ||
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| * The code doesn' | * The code doesn' | ||
| - | *The code was corrected on 2023.11.28.\\ The code used in the initial enumeration was discovered to contain a mistake related to GPU thread synchronization. Corrected versions of the code were used in the second enumeration. No erroneous | + | *The code was corrected on 2023.11.28.\\ The code used in the initial enumeration was discovered to contain a mistake related to GPU thread synchronization. Corrected versions of the code were used in the second enumeration. No erroneous |
| [[ms-20230918-m.c|Non-CUDA code in C using pthread]] (updated on 2023.09.18) | [[ms-20230918-m.c|Non-CUDA code in C using pthread]] (updated on 2023.09.18) | ||
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| ===== Semi-magic squares ===== | ===== Semi-magic squares ===== | ||
| - | The latest code used in the second enumeration counted semi-magic squares besides magic squares and produced the same result as discovered by a very different approach[5]. This match is considered as a cross verification of the counting method and of computing resources used in the calculation. All [[semi_magic_subtotals|subtotals of semi-magic (including magic) squares]] are available. | + | The latest code used in the second enumeration counted semi-magic squares besides magic squares and produced the same result as discovered by a very different approach |
| * 5. A. Ripatti, On the number of semi-magic squares of order 6, arXiv: | * 5. A. Ripatti, On the number of semi-magic squares of order 6, arXiv: | ||
magicsquare6.1718757764.txt.gz · Last modified: 2024/06/19 09:42 by mino