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The only possible sets are:
1089 324 576
3025 169 784
3025 196 784
3025 784 961
9025 361 784
9801 324 576
If I had either of the two solutions that had 324 and 576 plus a unique four-digit square, you'd have no way of differentiating which I had. Likewise if I had any of the three solutions that shared 784 and 3025, along with a unique other three-digit number, you'd have no way of telling which of those sets I had.
What's left is that I must have had 9025, 361 and 784, of which I shared 784 with Harry and Tom
This checks out as the only possibility for sharing one number with each of the other two players.
Indeed Harry and Tom must be two of the players who shared 3025 and 784, as, if I had said I shared no numbers in common you would not have been able to deduce the original question, as either of the players with 324 and 576 would share none in common with any of the 784 players and vice versa.
So I had 9025, 361 and 784 and the other two shared 3025 and 784.
This is Enigma 1401 from New Scientist for July 22-28, 2006. |
