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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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re: answer with proof / neater & corrected | Comment 2 of 4 |
(In reply to answer with proof by Daniel)

Let n = (2/3)*10^x + (1/3) = 6...67 [x-1 6's and one 7]

then n^2 = [(2/3)*10^x]^2 + 2*(2/3)*10^x*(1/3)+ (1/3)^2
= (4/9)*10^(2x) + (4/9)*10^x + 1/9
= 4...44...4.444... + 4...4.444... + 0.111...
=4...48...89 [x 4's followed by x-1 8's and one 9]

  Posted by Jer on 2013-07-27 14:14:38

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