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Fortune From Four (Posted on 2009-11-12) Difficulty: 3 of 5
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    
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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)

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*** Based on a problem by Susan Denham, which appeared on New Scientist No. 1998 (7 Oct 1995), in the Enigma problem section.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre(2): Logic and a little trial & 2 errorsBenjamin J. Ladd2009-11-19 15:50:44
Hints/Tipsre: Logic and a little trial & 2 errorsAdy TZIDON2009-11-13 16:44:42
SolutionSolutionDej Mar2009-11-12 23:19:29
SolutionLogic and a little trial & error:Benjamin J. Ladd2009-11-12 17:08:27
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