Substitute each of the capital letters by a different base ten digit from 0 to 8 to satisfy each of the following cryptarithmetic relationships.

• ABCDEFGF = A^E + B^E + C^E + D^E + E^E + F^E + G^E + F^E, where each of A and E is nonzero, and:


• ABCDEFGF does not contain the digit 1, and:
• Reading from left to right, odd digits appear in descending order of magnitude, but the nonzero even digits appear in ascending order of magnitude, in ABCDEFGF.

ABCDEFGF = 24,678,050 = 2^8 + 4^8 + 6^8 + 7^8 + 8^8 + 5^8

(I don't think the 3rd criterion is necessary, about the odd & even digits, because the above solution was the only one I found anyway.)

Posted by Jim Keneipp on 2010-01-24 14:58:04