In the planet Realmebon, the inhabitants use base 6 in their daily transactions. One of the inhabitants noticed that if he split his 6-digit ID number into two 3-digit numbers and squared each of them, their sum would equal his ID number.

How many possible ID numbers could he have been assigned, and what are they?

Brute force is giving me these eight results:

000000
010100
550100
000001
100213
500213
410244
150244

Maybe there is a clever way to find the solution, but computers are so fast nowadays...

Posted by JLo on 2006-11-11 15:22:12