Solve this alphametic, where each of the capital letters in bold denotes a different base 11 digit from 0 to A. None of the numbers contains a leading zero and U is even.

(TRY)² + (FOUR)² = (FIVE)²

(In reply to computer solution by Daniel)

By not specifying DEFDBL A-Z you are defaulting to only 7-decimal-digit precision (approximately as the numbers are kept in binary).

That leads to the false solution

792^2+ 3069^2= 3158^2

In decimal, you are claiming that 948^2 + 4068^2 = 4177^2. The squares of two even numbers cannot add to the square of an odd number.

In base 11, 3069 can be seen to be even as it has two odd digits. In base 11, count the number of odd digits; if that is odd the number is odd but if it is even the number is even, as all place values are odd: 1, 11, 121, etc.

Thus also, 3158 in base-11 is odd as it has three odd digits.

Edited on May 27, 2009, 1:13 pm

Posted by Charlie on 2009-05-27 13:11:57