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Three Digit Number Nuance (Posted on 2022-10-04)

Determine the (non-leading zero) 3-digit positive integer N such that the product of the digits of N is equal to N/5.

Source: Adapted from a problem appearing in a German Mathematical Olympiad.

*** Computer solutions are welcome, but an analytical solution is preferred.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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shortest?

Comment 3 of 3 |

a*b*c = (100a + 10b + c)/5 < 999/5 < 200 so a=1.

c=5 as noted, then 25b = 10b + 105 and b=7.

Posted by xdog on 2022-10-05 20:13:00

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