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The Trilogic Game
Feb. 27th, 2011 02:36 pmThere was a letter in The Independent today following on from an earlier article about a Doctor Who exhibition. The writer of the article remembered seeing an episode of Doctor Who in his childhood which the person showing him around the exhibition identified as The Celestial Toymaker. The letter writer suggests that from the description, it was more likely to have been Carnival of Monsters, something I thought when reading the article.
However, mention of The Celestial Toymaker brought back memories. About the only thing that I can remember about the episode was that the Doctor was having to solve a puzzle while his companions had to navigate a number of other games and puzzles. And the puzzle the Doctor had to solve was called the Trilogic Game. There was even an article about the game in the Radio Times, telling you how to play the game yourself at home.
It was played on a triangular board. In one corner sat a tetrahedral pyramid sliced horizontally into ten tiles, so the top tile was a smaller tetrahedron, below that a triangular tile with sloping edges, and so on down, the bottom tile being the largest. The object of the game was to transfer the tiles from one corner to another in 1023 moves. A move was taking the top tile from one corner and placing it in another. No tile could be placed on a smaller tile, but any tile could be placed on an empty corner.
Fans of recreational maths will know this as the Towers of Hanoi, a puzzle going back to Victorian times, but I'd never seen it before. When I did see it later in books o, I always thought this triangular packaging was more elegant than the normal presentation, in which the tiles are discs or rings placed on three pegs arranged in a straight line.
After the first part of the story was shown, I re-read the article in the Radio Times and set about trying the puzzle with materials to hand, mostly toys and pieces of paper. The article told me that the number of moves for three tiles was 7, for four tiles 15, up to 1023 for ten tiles. I quickly noticed that each number was twice the previous number plus one and that gave me the clue to solve the puzzle. (In fact, the number of moves for a pile of n tiles is 2^n -1 but I don't think I knew of powers of two then, although I had come across binary arithmetic.)
To move a pile of one tile from corner A to B is easy, of course. To move two tiles, move the top tile from A to C, the second to B, and then move the tile from C to B - three moves. For n tiles to be moved from A to B, move the top n-1 tiles from A to C, the nth tile from A to B, and then repeat the first set of moves to move the n-1 tiles from B to C.
According to Wikipedia, this story was broadcast in April 1966. More than ten years later, by which time I was working as computer programmer, we got a new computer at work that allowed recursive programming, and to test it, I wrote a program to play the Towers of Hanoi.
[Wrote this entry some days ago, and thought I'd posted it then, but it disappered, only for it to reappear just now.]
However, mention of The Celestial Toymaker brought back memories. About the only thing that I can remember about the episode was that the Doctor was having to solve a puzzle while his companions had to navigate a number of other games and puzzles. And the puzzle the Doctor had to solve was called the Trilogic Game. There was even an article about the game in the Radio Times, telling you how to play the game yourself at home.
It was played on a triangular board. In one corner sat a tetrahedral pyramid sliced horizontally into ten tiles, so the top tile was a smaller tetrahedron, below that a triangular tile with sloping edges, and so on down, the bottom tile being the largest. The object of the game was to transfer the tiles from one corner to another in 1023 moves. A move was taking the top tile from one corner and placing it in another. No tile could be placed on a smaller tile, but any tile could be placed on an empty corner.
Fans of recreational maths will know this as the Towers of Hanoi, a puzzle going back to Victorian times, but I'd never seen it before. When I did see it later in books o, I always thought this triangular packaging was more elegant than the normal presentation, in which the tiles are discs or rings placed on three pegs arranged in a straight line.
After the first part of the story was shown, I re-read the article in the Radio Times and set about trying the puzzle with materials to hand, mostly toys and pieces of paper. The article told me that the number of moves for three tiles was 7, for four tiles 15, up to 1023 for ten tiles. I quickly noticed that each number was twice the previous number plus one and that gave me the clue to solve the puzzle. (In fact, the number of moves for a pile of n tiles is 2^n -1 but I don't think I knew of powers of two then, although I had come across binary arithmetic.)
To move a pile of one tile from corner A to B is easy, of course. To move two tiles, move the top tile from A to C, the second to B, and then move the tile from C to B - three moves. For n tiles to be moved from A to B, move the top n-1 tiles from A to C, the nth tile from A to B, and then repeat the first set of moves to move the n-1 tiles from B to C.
According to Wikipedia, this story was broadcast in April 1966. More than ten years later, by which time I was working as computer programmer, we got a new computer at work that allowed recursive programming, and to test it, I wrote a program to play the Towers of Hanoi.
[Wrote this entry some days ago, and thought I'd posted it then, but it disappered, only for it to reappear just now.]
