perplexus.info :: Numbers : Digital Product Triples

Digital Product Triples (Posted on 2023-09-05)

The digital product P(N) of an integer N is the product of its decimal digits.

For example, P(128)=16.

Find all sets of three positive integers A, B and C such that:
A = P(B)+P(C)
B = P(A)+P(C)
C = P(A)+P(B).

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

There are only three sets that satisfy the given conditions, and these are:
(A,B,C) (- (5,5,10), (36,36,36), (498,498,576) so that:
All possible triplets are given by:
(A,B, C) = (5,5,10), (5,10,5), (10,5,5), (498, 498, 576), (498,576,498), (576,498, 498), and (36,36,36)
For an explanation, refer to the solutions submitted by Charlie and Larry here and here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(2): Computer solution	Larry	2023-09-06 05:38:31
re: Computer solution	Charlie	2023-09-05 21:20:49
Computer solution	Larry	2023-09-05 10:52:53
computer findings	Charlie	2023-09-05 09:35:07

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