3 ms·

A weird version of tic-tac-toe my friends and I came up with years ago: you play without a board. Any move is valid so long as you could superimpose a standard

A weird version of tic-tac-toe my friends and I came up with years ago: you play without a board. Any move is valid so long as you could superimpose a standard tic-tac-toe grid over the results. (You assume the marks are at the center of their respective squares; you allow the board to be at any scale or angle, but you can't skew it.) The first two moves have no constraint, so you can just start with an X and O already on the board. And after a few moves there might be only one implied board possible, after which it reduces to the normal game. But I always thought it was an interesting twist.

lotharbot 13y ago
Somebody posted another tic tac toe variant on HN some time ago, where the squares were numbered 1-9 and the goal was to get any three squares that summed to 15. It turns out this is equivalent to playing tic tac toe with sides that wrap around (like a torus).
- gohrt 13y ago
  also equivalent to covering every row and column on the board.
- Someone 13y ago
  No, that's 100% equivalent to tic tac toe (http://en.wikipedia.org/wiki/Tic-tac-toe#Variations http://en.wikipedia.org/wiki/Tic-tac-toe#Variations) (To see why no torus version exists: on a '3x3' torus, all squares are identical, so you have must four ways to get three in a row from each starting number. Also, the row/column/diagonal sum must be 15. However, starting with 9, there are only two ways to get 15 with: 1 and 5 and 2 and 4) The variant with nine words, where selecting three words that share a letter wins the game, IMO is even better.
  - lotharbot 13y ago
    I may have misremembered the details of the game, or conflated it with another game. What I remember clearly is that the game was equivalent of tic tac toe on a torus -- one could win with a "diagonal" of the form .|x|. x|.|. .|.|x as well as any of the traditional tic tac toe win conditions.
    - Someone 13y ago
      Tic tac toe on toruses is fairly popular as an educational toy, and there also is serious research on it, for example http://www.ux1.eiu.edu/~kwolcott/TTT.pdf http://www.ux1.eiu.edu/~kwolcott/TTT.pdf. You might have mixed the 'on a torus' part with the 'using a magic square' part. No problem, but the two do not mix that way (maybe, on larger boards? That 4x4 Dürer square (http://mathworld.wolfram.com/DuerersMagicSquare.html http://mathworld.wolfram.com/DuerersMagicSquare.html) has zillions of 'add up to 34' sets of cells. There may be even better ones of larger size)

lotharbot 13y ago

Somebody posted another tic tac toe variant on HN some time ago, where the squares were numbered 1-9 and the goal was to get any three squares that summed to 15. It turns out this is equivalent to playing tic tac toe with sides that wrap around (like a torus).

gohrt 13y ago
also equivalent to covering every row and column on the board.
Someone 13y ago
No, that's 100% equivalent to tic tac toe (http://en.wikipedia.org/wiki/Tic-tac-toe#Variations http://en.wikipedia.org/wiki/Tic-tac-toe#Variations) (To see why no torus version exists: on a '3x3' torus, all squares are identical, so you have must four ways to get three in a row from each starting number. Also, the row/column/diagonal sum must be 15. However, starting with 9, there are only two ways to get 15 with: 1 and 5 and 2 and 4) The variant with nine words, where selecting three words that share a letter wins the game, IMO is even better.
- lotharbot 13y ago
  I may have misremembered the details of the game, or conflated it with another game. What I remember clearly is that the game was equivalent of tic tac toe on a torus -- one could win with a "diagonal" of the form .|x|. x|.|. .|.|x as well as any of the traditional tic tac toe win conditions.
  - Someone 13y ago
    Tic tac toe on toruses is fairly popular as an educational toy, and there also is serious research on it, for example http://www.ux1.eiu.edu/~kwolcott/TTT.pdf http://www.ux1.eiu.edu/~kwolcott/TTT.pdf. You might have mixed the 'on a torus' part with the 'using a magic square' part. No problem, but the two do not mix that way (maybe, on larger boards? That 4x4 Dürer square (http://mathworld.wolfram.com/DuerersMagicSquare.html http://mathworld.wolfram.com/DuerersMagicSquare.html) has zillions of 'add up to 34' sets of cells. There may be even better ones of larger size)