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 Fortune From Four (Posted on 2009-11-12)
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.

 Submitted by K Sengupta No Rating Solution: (Hide) The number represented by FORTUNE is 3701284. For a detailed explanation, refer to the solution submitted by Benjamin J. Ladd in this location. *** There was a small typo in Ladd's solution in the 3rd line from the end, and it should be as follows: FOUR: 3720 (+1 = 61^2) (iii) ------------------------------------------------------------------------------ *** Based on a problem by Susan Denham, which appeared on New Scientist No. 1998 (7 Oct 1995), in the Enigma problem section.

 Subject Author Date re(2): Logic and a little trial & 2 errors Benjamin J. Ladd 2009-11-19 15:50:44 re: Logic and a little trial & 2 errors Ady TZIDON 2009-11-13 16:44:42 Solution Dej Mar 2009-11-12 23:19:29 Logic and a little trial & error: Benjamin J. Ladd 2009-11-12 17:08:27

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