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Squarely Sorted (Posted on 2013-07-27) Difficulty: 3 of 5
An integer n, such as 1128, is called "sorted" if its digits are in sorted order. Find the largest integer n such that both n and n2 are sorted.

No Solution Yet Submitted by Danish Ahmed Khan    
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even more generally Comment 4 of 4 |
(In reply to more generally by Charlie)

There seem to be three infinite categories that satisfy the criterion:

333...333666...6667 where there are zero or more 3's, zero or more 6's and a 7.

333...3334 or 333...3335 where there are zero or more 3's.

1666...6667 where there are zero or more 6's.

The only fitting numbers that don't fit these categories seem to be:

 n   n^2
116 13456
117 13689
12  144
13  169
15  225
16  256

The largest such sporadic n would then be 117.


  Posted by Charlie on 2013-07-28 09:34:33
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