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Square Settlement With Digits (Posted on 2016-04-07) Difficulty: 3 of 5
M is a perfect square whose 2nd and 3rd digits are 20 and the last two digits are 16.

Find the three smallest values of M.

No Solution Yet Submitted by K Sengupta    
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Solution Ten solutions | Comment 1 of 2
Using a bit of brute force I ended up finding the smallest ten values of M.

The square of a number ends in 16 only if the number ends in 04, 46, 54, or 96.  I searched by a table using each ending separately.  Surprisingly the smallest 3 all come from the last ending.  

In order:
1096^2=1201216
4696^2=22052416
9596^2=92083216
10996^2=120912016
14846^2=220403716
14554^2=220641316
17896^2=320266816
17904^2=320553216
20496^2=420086016
20504^2=420414016

  Posted by Jer on 2016-04-07 14:02:58
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