perplexus.info :: Just Math : AABBCC and Perfect Square

AABBCC and Perfect Square (Posted on 2016-11-09)

N is a perfect square such that the last six digits of N is of the form AABBCC where A, B and C are distinct base ten digits and A is nonzero.

Find the smallest value of N.

What if C shouldn't be zero?

** AABBCC represents the concatenation of the digits and not their product.

*** For an extra challenge solve this puzzle without using a computer program.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

better solution

| Comment 5 of 6 |

You two were quick. I was just going to edit my other post but I'd better post anew.

the squares of 12, 38, 62, 88 all end with 44.

Checking 100n+12, 100n+38, 100n+62 yields a smaller solution:

2262^2=5116644

I'm not sure if that proves I've found the smallest, although Charlie's solution confirms it.

Posted by Jer on 2016-11-09 13:49:09

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