Each of the capital letters in bold denotes a different base ten digit from 0 to 9 to satisfy each of the following alphametic relationships. None of the numbers can contain any leading zero.

(i) ONE is a perfect square and:

(ii) Precisely one of TWO, THREE and FOUR is a perfect square, and:

(iii) Precisely one of TWO + 1, THREE + 1 and FOUR + 1 is a perfect square, and:

(iv) Precisely one of TWO + 2, THREE + 2 and FOUR + 2 is a perfect square.

Determine the number that is represented by FORTUNE.

ONE   :   784     =  28²
TWO   :   167 + 2 =  13²
THREE : 19044 + 0 = 138²
FOUR  :  3720 + 1 =  61²

0 1 2 3 4 5 6 7 8 9
R T U F E - W O N H

FORTUNE = 3701284

Posted by Dej Mar on 2009-11-12 23:19:29