Substitute each of the capital letters in bold by a different base ten digit from 0 to 9, such that:

• THAT is a perfect square, and none of T and I is zero, and:
• The base ten representation of the product (THIS)*(THAT)*(IT) has no leading zeroes and contains each of the digits from 0 to 9 exactly once.

For the product to be a 10 digit number T must be from 3 to 9.
Since THAT is a Square number T must also be 4,5, 6 or 9.
In the range from 4000 to 9999 there are just 3 squares whose first and last digits are the same, 4624, 5625 and 9409.

Taking the values of each of those squares in turn only the values of I and S need to be found.  By cycling through values for those only 5625 as the square and 93 for the value of IS satisfy the requirements:
5693 * 5625 * 95 = 3,042,196,875.

Posted by brianjn on 2009-06-19 22:31:20