Determine the respective values of SQUARE and CUBE, given that SQUARE is a perfect cube and CUBE is a perfect square. Each of the capital letters in bold denotes a different decimal digit from 0 to 9 and neither C nor S can be zero.

firstly, we're working with a pretty finite set of possibilities - six-digit cubes and four-digit squares.  Eliminate the ones that have any digit in them more than once.  Compare the two sets of results with each other and eliminate those that end in a digit with which none of the numbers in the other set end.  From there its a pretty simple task of eliminating digit combinations that don't fit the pattern for the U and E.  You're left with:

SQUARE = 328509 (69^3)
CUBE = 1849 (43^2)

(by the way, MS Excel helps a lot.)

Edited on August 4, 2009, 12:46 pm

Posted by Sing4TheDay on 2009-08-04 12:45:24