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My favorite numbers III (Posted on 2010-03-04) Difficulty: 4 of 5
Determine all possible octuplets (A, B, C, D, E, F, G, H) of positive integers, with A ≤ B ≤ C ≤ D, and, E ≤ F ≤ G ≤ H and, A ≤ E, that satisfy both the equations: A+B+C+D = E*F*G*H and, A*B*C*D = E+F+G+H.

Prove that these are the only octuplets that exist.

No Solution Yet Submitted by K Sengupta    
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re: As simple as possible, but no simpler... | Comment 3 of 6 |
(In reply to As simple as possible, but no simpler... by ed bottemiller)

Format problem on the last posting

1+1+1+9 = 12 = 1 * 1 *3 * 4

1 * 1 * 1 * 9 = 9 = 1+1+3+4

Or, if "integers"  need not be single digits:

e.g. (1,1,1,11) and (1,1,2,7)

1+1+1+11 = 14 = 1 * 1 * 2 * 7

1 * 1 * 1 * 11 = 11 = 1+1+2+7

and others.   


  Posted by ed bottemiller on 2010-03-04 17:51:18
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