perplexus.info :: Numbers : Digital Product Triples

Home > Numbers

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).

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: Computer solution

| Comment 3 of 4 |

(In reply to Computer solution by Larry)

To be clear, for (A,B,C)=(5,5,10)

P(A)=5

P(B)=5

P(C)=0

P(A)+P(B)=10=C

P(B)+P(C)=5 = A

P(C)+P(A)=5 = B

and each of A, B, and C is positive. The P values need not be positive.

Posted by Charlie on 2023-09-05 21:20:49

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info