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