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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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As simple as possible, but no simpler... | Comment 2 of 6 |

I don't think this problem is that simple.  The first question is whether "integer" is limited to "digits", or does it include any whole numbers.  It is not required that the same numbers of used.

Consider (1,1,1,9) and (1,1,3,4):

1+1+1+9

= 9 
  Posted by ed bottemiller on 2010-03-04 17:43:30
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