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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.)

computer findings

| Comment 1 of 4

for a=1:222

for b=a:222

for c=b:222

if a==pod(b)+pod(c)

if b==pod(a)+pod(c)

if c==pod(b)+pod(a)

disp([a b c])

end

where pod is

function pd = pod(n)

dgts=num2str(n) ;

pd=prod(dgts-'0');

end

>> digitalProductTriples

5 5 10

36 36 36

These are the only two sets. Of course in the first, the 10 could be any of A, B or C.

Posted by Charlie on 2023-09-05 09:35:07

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