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Consider The Relation, Sum Positive Integers (Posted on 2008-02-12) Difficulty: 2 of 5
Each of F, G and H are positive integers such that:

FGH* GHF* HFG = 5*F*G*H

Determine the possible value(s) that F+G+H can assume.

Note: For a precise interpretation of the value of ABC, refer to the wikipedia article on exponentiation in this location.

See The Solution Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 2 of 4 |
(F, G, H) => {(1, 5, 2), (2, 1, 5), (5, 2, 1)}

152*215*521 = 125*21*52 = 1*2*25 = 50

(5)*1*5*2 = 50

[F + G + H] = 8

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Note, though only 1, 2, and 5 are the integers that are the solutions for (F, G, H), not all arrangements of 1, 2, and 5 are, e.g., for (1, 2, 5)...
125*251*512 = 132*25*51 = 1*32*5 = 160

Edited on February 12, 2008, 1:38 pm
  Posted by Dej Mar on 2008-02-12 13:38:02

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