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