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Testy Triplet Treat (Posted on 2013-08-04) Difficulty: 3 of 5
P(N) denotes the product of the digits in the base ten representation of N.

Determine all possible triplets (A,B,C) of positive integers with A ≤ B ≤ C that satisfy this system of equations:

A = P(B)+ P(C), B = P(A) + P(C), and C = P(A) + P(B)

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re(2): results so far, but no proof in sight | Comment 6 of 7 |
(In reply to re: results so far, but no proof in sight by Charlie)

For my intuition it is enough,  for a finicky purist NO...

I wonder, what proof will be presented in the "official" solution.

  Posted by Ady TZIDON on 2013-08-05 11:09:33
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