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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	Subject	Author	Date
	re(2): results so far, but no proof in sight	Charlie	2013-08-06 10:07:34
	re(2): results so far, but no proof in sight	Ady TZIDON	2013-08-05 11:09:33
	re: results so far, but no proof in sight	Charlie	2013-08-05 09:50:41
	re(3): results so far, but no proof in sight	Daniel	2013-08-04 15:42:58
	re(2): results so far, but no proof in sight	Ady TZIDON	2013-08-04 15:25:36
	re: results so far, but no proof in sight	Charlie	2013-08-04 12:55:17
	results so far, but no proof in sight	Charlie	2013-08-04 12:53:46