Solve this alphametic, where each of the capital letters in bold represents a different decimal digit from 0 to 9. None of the numbers contains any leading zero.

(TO)! = (KNOW)*(TITANS)

(In reply to Spreadsheet only as a Calculator by brianjn)

I used the same logic to determine TO! = 12! = 479001600.
And S or W = 5 and W or S = 0, 4, 6, or 8.
I then factored 12! = 2^10 * 3^5 * 5^2 * 7 * 11. 
Assuming KNOW ended in 25 and no even prime factor (i.e. 2), I determined the factors to KNOW would be 3^3 * 5^2 * 7 = 4725 to have a four digit number >= 3725. This left the remaining factors 2^10 * 3^2 * 11 = 101376. These numbers fit the alphametric.

12! = 4725 * 101376
TO! = KNOW * TITANS

 

Edited on July 18, 2009, 1:58 pm

Posted by Dej Mar on 2009-06-14 23:53:47