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.

(In reply to Logic and a little trial & error: by Benjamin J. Ladd)

TWO:  167 (13^2 + 2) (iv)====> 167 =13^2 - 2

THREE:  19044 (138^2) (ii)======>ok

FOUR:  3720 (61^2 + 1) (iii)====>3720 =61^2 - 1  (iii)

 

 

Your solution is correct   

Posted by Ady TZIDON on 2009-11-13 16:44:42