Pyramid PuzzleIt is known that
|n2 = 4900 = 702|
|n2 = M2|
But supposing the balls in each layer were stuck together. Would it be possible to arrange these 24 squares to make the 70 × 70 square. The following applet has been written to test this out.
Be warned that the puzzle is almost certainly impossible. Indeed, examples of fitting any set of squares together to make a larger square are hard to find. But I thought it was worth writing this applet to see what could be done. Even if the full puzzle is impossible, it might be interesting to see whether it is possible to make a smaller square using some of the pieces available. If you do this then do let me know at :
I would also be interested to hear about any proofs of the impossibility of the puzzle.
If you have 4900 balls to spare then you might like to try making a physical version of this puzzle, although I guess it would take up quite a bit of space.
Note: Apparently the puzzle was in fact been shown to be impossible in 1975. Further details are available at http://home.datacomm.ch/t_wolf/tw/misc/squares.html