The Pentomino Puzzle (and Tetris) - Numberphile
video description
Golomb is perhaps at least as great a genius as Dudeney, but probably wouldn't have been without Dudeney.
I've been playing with polyominoes (and other similar shapes) since I was a kid.
Date: 2022-04-08
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Comments and reviews: 9
mstmar
I remember we had one of those games as a kid. Every time one of us solved it, we would compare it to other solutions. If it was a new one, we would put a piece of paper over it and rub a pencil over it to keep a record. In the end we had something like 30 solutions, not counting rotations, reflections, and simple swaps (like in the solution given, if you swap the + with the one below it, you get another solution. I doubt we got them all, but still a fun game.
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I remember we had one of those games as a kid. Every time one of us solved it, we would compare it to other solutions. If it was a new one, we would put a piece of paper over it and rub a pencil over it to keep a record. In the end we had something like 30 solutions, not counting rotations, reflections, and simple swaps (like in the solution given, if you swap the + with the one below it, you get another solution. I doubt we got them all, but still a fun game.
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Magician
A bit surprised they didn't mention the story about how when Tetris was being created it was originally going to be with pentominoes instead of tetrominoes, but it was thought to be a bit hard because of the more complex shapes and wider variety compared to tetrominoes.
(Also another fun fact: Tetris is a portmanteau of -tetra- (four) and -tennis- which was the creator's favourite sport at the time)
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A bit surprised they didn't mention the story about how when Tetris was being created it was originally going to be with pentominoes instead of tetrominoes, but it was thought to be a bit hard because of the more complex shapes and wider variety compared to tetrominoes.
(Also another fun fact: Tetris is a portmanteau of -tetra- (four) and -tennis- which was the creator's favourite sport at the time)
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Robert
There's a game called Spear's Multipuzzle, which uses all the hexominoes (all the shapes made of six squares. There's a 6 by 10 rectangle to fit ten hexominoes in. Some shapes you get two of, such as a 1x6 straight line. The instructions have 48 combinations telling you which pieces to use and the easy ones show where one or two pieces go. However, on my copy someone wrote in a 49th combination.
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There's a game called Spear's Multipuzzle, which uses all the hexominoes (all the shapes made of six squares. There's a 6 by 10 rectangle to fit ten hexominoes in. Some shapes you get two of, such as a 1x6 straight line. The instructions have 48 combinations telling you which pieces to use and the easy ones show where one or two pieces go. However, on my copy someone wrote in a 49th combination.
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Graham
If you write down your solution and try again you will find that the next solutions is different. At a hostel in New Zealand in 1988 they had a book with solutions that people had found. There were over a hundred unique solutions. During my stay I solved it several times, but none of my solutions had already been recorded. Therefore it is logical to assume that there are many many more.
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If you write down your solution and try again you will find that the next solutions is different. At a hostel in New Zealand in 1988 they had a book with solutions that people had found. There were over a hundred unique solutions. During my stay I solved it several times, but none of my solutions had already been recorded. Therefore it is logical to assume that there are many many more.
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Zack
Apparently this puzzle has over 16 thousand different solutions (disregarding rotations and reflections, but I couldn't help but notice that the decision to make the leftover 4 squares into a 2 by 2 tetromino seemed a bit arbitrary. Has anyone ever looked into how the number of solutions is different if the leftover 4 squares are built into a different tetromino?
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Apparently this puzzle has over 16 thousand different solutions (disregarding rotations and reflections, but I couldn't help but notice that the decision to make the leftover 4 squares into a 2 by 2 tetromino seemed a bit arbitrary. Has anyone ever looked into how the number of solutions is different if the leftover 4 squares are built into a different tetromino?
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kentrel2
The Talos Principle is a video game that uses these puzzles. It's a brilliant Portal-style game where you collect these pieces as rewards for solving each level. Then you have to solve the puzzle to unlock the next levels. It sticks to Tetris shapes only. I found I could solve even the hardest just by moving them randomly without much planning.
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The Talos Principle is a video game that uses these puzzles. It's a brilliant Portal-style game where you collect these pieces as rewards for solving each level. Then you have to solve the puzzle to unlock the next levels. It sticks to Tetris shapes only. I found I could solve even the hardest just by moving them randomly without much planning.
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Quinn
Pentis: Pentominoes(5) 18 [including mirror images]
Tetris: Tetrominoes(4) 7 [including mirror images]
Tris: Trominoes(3) 2
Dis: Dominoes(2) 1
His: Hominoes(1) 1
Udis: Udominoes(0) 1
Unhis: Unhominoes(-1)?
Undis: Undominoes(-2)?
Untris: Untrominoes(-3)?
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Pentis: Pentominoes(5) 18 [including mirror images]
Tetris: Tetrominoes(4) 7 [including mirror images]
Tris: Trominoes(3) 2
Dis: Dominoes(2) 1
His: Hominoes(1) 1
Udis: Udominoes(0) 1
Unhis: Unhominoes(-1)?
Undis: Undominoes(-2)?
Untris: Untrominoes(-3)?
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Daniel
It's unclear what metrics (for -depth- and -variety-) by which Dudeney's considered -the greatest the world has ever seen- in terms of dreaming up mathematical puzzles.
With all due credit to Dudeney and Lloyd, -Paul Erdos- was known to have posed some pretty deep puzzles.
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It's unclear what metrics (for -depth- and -variety-) by which Dudeney's considered -the greatest the world has ever seen- in terms of dreaming up mathematical puzzles.
With all due credit to Dudeney and Lloyd, -Paul Erdos- was known to have posed some pretty deep puzzles.
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tropezando
Not quite the same puzzle, but a game called Blokus uses all configurations of one square up to pentominoes, touching corners to claim space on a grid. It's a great game for both adults and kids and I recommend it for people who like puzzles, strategy, and competition.
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Not quite the same puzzle, but a game called Blokus uses all configurations of one square up to pentominoes, touching corners to claim space on a grid. It's a great game for both adults and kids and I recommend it for people who like puzzles, strategy, and competition.
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