The letters A, D, E, J, M, N, O, V and Z each represent a different digit between 0 and 9. (One digit is not used.)

DAVE, ZENA, JOE and MO are all square numbers. Can you find them?

This problem developed from a blunder I made when trying to solve Charlie's Portuguese Squares puzzle.

DAVE = 2401 = 49 squared

ZENA = 5184 = 72 squared

JOE = 961 = 31 squared

MO = 36 = 6 squared

A=4, D=2, E=1, J=9, M=3, N=8, O=6, V=0, Z=5

Method: Generate possible values for MO (m,o); then generate possible values for JOE (j,e); then generate possible values for ZENA (z,n,a); then generate possible values for DAVE (d,v).  Nine imbedded loops. Single solution.

Suggestion: For all of these letter/digit substitutions, it should be explicitly stated that no number begins with zero. I assumed this, i.e. the D, Z, J, and M could not be zero, since each begins a word.

Posted by ed bottemiller on 2008-04-22 12:55:48