perplexus.info :: Numbers : Digit permutation

Digit permutation (Posted on 2013-03-03)

735 is a 3-digit base ten positive integer formed by a permutation of the digits 3, 5 and 7 and, 735 is divisible by each of 3, 5 and 7.

Determine the minimum value of N with N ≥ 11 such that there exists a 3-digit base-N positive integer p which is formed by a permutation of the digits 3, 5 and 7 such that p is divisible by each of 3, 5 and 7. What is the next smallest value of N with this property?

No Solution Yet Submitted by K Sengupta

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Excel solution (spoiler)

| Comment 1 of 3

I get 753 (base 19) as being divisible by 105 base 10.

753 base 19 = 2625 base 10 = 25*3*5*7

So the solution is that N = 19

Also 537 base 26 = 3465 = 33*3*5*7

And base 31 is interesting, because both 357 and 735 work

Other bases with two solutions are base 61, 91, 136 and base 166

Posted by Steve Herman on 2013-03-03 10:50:47

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