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?

There exists a list of six sets (with two 3-digit and one 4-digit) of perfect squares that will each contain all the digits 0 - 9.  They are:

169   784   3025
196   784   3025
961   784   3025
361   784   9025
324   576   1089
324   576   9801

Five share two squares (three with 28² & 55² and two with 18² & 24²) and one with one square (28²).  The set with a single common square, 361 784 9025, with the squares 19², 28², and 95², must then be your solution.  Harry and Tom, given by deduction that they share your square, share the two squares 28² & 55².

Posted by Dej Mar on 2006-09-01 12:27:34