Harry, Tom and I each found a four-digit perfect square and two three-digit perfect squares that among them used all the digits 0 - 9. No two solutions were identical. If I told you how many squares my solution had in common with each of the other two, you could deduce which squares formed my solution.

Which squares formed my solution?

Which square or squares (if any) did Harry's and Tom's solutions have in common?

your solution: 361, 784 and 9025.
harry and tom solutions: 324, 576 and 1089; 324, 576 and 9801.

tom and harry had two squares in common between them (324 and 576). you had none in common with them (should you tell you had anything in common it would be impossible to tell which set was yours).

method used (a rather dull method... there should be easier and more methodic ways to solve this):

- take out from the 3 digit perfect squares list those which have repeated digits;
- do the same with the four digit;
- build a list of pairs of 3 digit squares, having in mind that they can't repeat the same digits between them;
- now, with the list of pairs, build up a list of the four missing digits for each pair;
- cut out all four digit squares that don't have a 0 (since all the 3 digit squares ask for a missing 0);
- compare the missing digits list with the available four digit squares;
- et voila, you have three possible combinations;
- you'll have to chose the one which hasn't anything in common with the other two, as explained above.

(oh dear, i'm waiting for the quick and methodic way to solve this... :>)

Posted by vj on 2006-09-01 09:13:14