PentoCoin: Difference between revisions

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== History ==

In October 2022, the NFT collection ''[https://opensea.io/collection/pentocoin NFT PentoCoin]'' was created and listed on [[OpenSea]].<ref>~~{{cite news|title=PentoCoin|url=~~https://opensea.io/collection/pentocoin~~|accessdate=9 June 2023|publisher=opensea.io|date=}}~~</ref> The first item from the collection is given on the ''Opensea'' platform.<ref>~~{{cite news|title=PentoCoin #1 2 3 4 5 6 7 8 9 10 11 12~~

In October 2022, the NFT collection ''[https://opensea.io/collection/pentocoin NFT PentoCoin]'' was created and listed on [[OpenSea]].<ref>[https://opensea.io/collection/pentocoin "PentoCoin"]</ref> The first item from the collection is given on the ''Opensea'' platform.<ref>[https://opensea.io/assets/ethereum/0x495f947276749ce646f68ac8c248420045cb7b5e/23467797326275027743874371014149683281019546929197637997700847618907801911297 "PentoCoin #1 2 3 4 5 6 7 8 9 10 11 12"]</ref>

~~|url=~~https://opensea.io/assets/ethereum/0x495f947276749ce646f68ac8c248420045cb7b5e/23467797326275027743874371014149683281019546929197637997700847618907801911297~~|accessdate=~~9 ~~June 2023|publisher=opensea.io|date=}}~~</ref>

== Overview ==

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P(12, 12) = 12! / (12 - 12)! = 12! Where "!" denotes factorial. Let's calculate it:12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 479,001,600

The 6×10 case was first solved in 1960 by [[Colin Brian Haselgrove]] and [[Jenifer Haselgrove]].<ref>~~{{cite journal |author=C. B. Haselgrove |author2=Jenifer Haselgrove |date=October 1960 |title=A Computer Program for Pentominoes |journal=~~[~~[Eureka (University of Cambridge magazine)|Eureka]] |volume=23 |pages=16–18|url=~~https://www.archim.org.uk/eureka/archive/Eureka-23.pdf}}</ref> There are exactly 9356 solutions, including trivial variations obtained by rotation and reflection of the whole rectangle and including rotation and reflection of a subset of pentominoes (which sometimes provides an additional solution in a simple way). The 5×12 box has 4040 solutions, the 4×15 box has 1472 solutions, and the 3×20 box has just 8 solutions. In total, there are 14,876 combinations of pentomino shapes.

The 6×10 case was first solved in 1960 by [[Colin Brian Haselgrove]] and [[Jenifer Haselgrove]].<ref>[https://www.archim.org.uk/eureka/archive/Eureka-23.pdf "A Computer Program for Pentominoes"]</ref> There are exactly 9356 solutions, including trivial variations obtained by rotation and reflection of the whole rectangle and including rotation and reflection of a subset of pentominoes (which sometimes provides an additional solution in a simple way). The 5×12 box has 4040 solutions, the 4×15 box has 1472 solutions, and the 3×20 box has just 8 solutions. In total, there are 14,876 combinations of pentomino shapes.

However, there are certain combinations of pentomino shapes that share the same combination of numbers. These combinations have a property called "sibling," where multiple different shape combinations correspond to a single combination of numbers. The creator of the NFT PentoCoin collection, [https://www.facebook.com/attewood Alex Carolus Rex Attewood], calculated that there are a total of 14,153 digit combinations that yield solutions for pentomino. Therefore, the probability of a 12-digit combination being a solution for pentomino is 0.00295204% (14,153 out of 479,001,600).

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 == History ==
-In October 2022, the NFT collection ''[https://opensea.io/collection/pentocoin NFT PentoCoin]'' was created and listed on [[OpenSea]].<ref>{{cite news|title=PentoCoin|url=https://opensea.io/collection/pentocoin|accessdate=9 June 2023|publisher=opensea.io|date=}}</ref> The first item from the collection is given on the ''Opensea'' platform.<ref>{{cite news|title=PentoCoin #1 2 3 4 5 6 7 8 9 10 11 12
+In October 2022, the NFT collection ''[https://opensea.io/collection/pentocoin NFT PentoCoin]'' was created and listed on [[OpenSea]].<ref>[https://opensea.io/collection/pentocoin "PentoCoin"]</ref> The first item from the collection is given on the ''Opensea'' platform.<ref>[https://opensea.io/assets/ethereum/0x495f947276749ce646f68ac8c248420045cb7b5e/23467797326275027743874371014149683281019546929197637997700847618907801911297 "PentoCoin #1 2 3 4 5 6 7 8 9 10 11 12"]</ref>
-|url=https://opensea.io/assets/ethereum/0x495f947276749ce646f68ac8c248420045cb7b5e/23467797326275027743874371014149683281019546929197637997700847618907801911297|accessdate=9 June 2023|publisher=opensea.io|date=}}</ref>
 == Overview ==
@@ Line 18: / Line 17: @@
 P(12, 12) = 12! / (12 - 12)! = 12! Where "!" denotes factorial. Let's calculate it:12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 479,001,600
-The 6×10 case was first solved in 1960 by [[Colin Brian Haselgrove]] and [[Jenifer Haselgrove]].<ref>{{cite journal |author=C. B. Haselgrove |author2=Jenifer Haselgrove |date=October 1960 |title=A Computer Program for Pentominoes |journal=[[Eureka (University of Cambridge magazine)|Eureka]] |volume=23 |pages=16–18|url=https://www.archim.org.uk/eureka/archive/Eureka-23.pdf}}</ref> There are exactly 9356 solutions, including trivial variations obtained by rotation and reflection of the whole rectangle and including rotation and reflection of a subset of pentominoes (which sometimes provides an additional solution in a simple way). The 5×12 box has 4040 solutions, the 4×15 box has 1472 solutions, and the 3×20 box has just 8 solutions. In total, there are 14,876 combinations of pentomino shapes.
+The 6×10 case was first solved in 1960 by [[Colin Brian Haselgrove]] and [[Jenifer Haselgrove]].<ref>[https://www.archim.org.uk/eureka/archive/Eureka-23.pdf "A Computer Program for Pentominoes"]</ref> There are exactly 9356 solutions, including trivial variations obtained by rotation and reflection of the whole rectangle and including rotation and reflection of a subset of pentominoes (which sometimes provides an additional solution in a simple way). The 5×12 box has 4040 solutions, the 4×15 box has 1472 solutions, and the 3×20 box has just 8 solutions. In total, there are 14,876 combinations of pentomino shapes.
 However, there are certain combinations of pentomino shapes that share the same combination of numbers. These combinations have a property called "sibling," where multiple different shape combinations correspond to a single combination of numbers. The creator of the NFT PentoCoin collection, [https://www.facebook.com/attewood Alex Carolus Rex Attewood], calculated that there are a total of 14,153 digit combinations that yield solutions for pentomino. Therefore, the probability of a 12-digit combination being a solution for pentomino is 0.00295204% (14,153 out of 479,001,600).