Clever Learning blog

Conway's Soldiers - a mind-bending puzzle

By Mark Bensilum. 25/4/17

Click for interactive game

Conway's Soldiers is a mathematical problem first posed by John Conway in 1961. The challenge is to move tiles around on a never-ending checkerboard and move them as high up the board as you can. Just like the game solitaire, you move a tile by jumping it over a neighbouring tile vertically or horizontally, and then removing the tile that you jumped over.

Conway's Soldiers grid

What's so mind-bending about that?

Even though the checkerboard extends infinitely in all directions, and you can move as many tiles as you like, it is impossible to get a tile more than four rows above where they started (unless you use an infinite number of moves). Intuitively, you'd like to think that with all those tiles to use, you could bring enough in to where you need them to do the job. But you can't!

The puzzle rose to prominence again in 2003, when it featured in Mark Haddon's excellent novel 'The curious incident of the dog in the night-time'. The main character, Christopher, runs through the puzzle mentally, to take his mind off other pressing matters.

I wanted to try this out for myself but was unable to find an interactive version anywhere, so I wrote one of my own. I used the excellent Processing software package to develop the first version, but then re-wrote it in JavaScript as this is faster and more responsive online.

Game of life animation by Bill Gosper

Conway is perhaps more famous for his beautiful 'Game of life' - a simulation of cellular life that follows very simple rules but can show wonderfully elegant outcomes.

Please send a comment and I will add it to the page


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