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 A square (Posted on 2004-06-25)
A number AABB is the square of an integer. Find this integer, aided by pen and paper. No other calculating aids allowed.

 Submitted by Ady TZIDON Rating: 3.1429 (7 votes) Solution: (Hide) Answer: 7744=88*88 It is easy as soon as you perceive that A+B=11 Remark: clearly AABB is divisible by 11, hence by 121. so A0B is also divisible by 11. For any number to be divisible by 11 , one evaluates two sums: SO - the sum of all the digits found on the odd-numbered places , and SE -the sum of all the digits found on the even-numbered places . The absolute value of SO-SE has to be divisible by 11. Hence A+B=11. There are only 2 possibilities for a square to be terminated by two identical digits ==> BB IS EITHER 00 or 44. Hence the answer 7744=88^2 ady

 Subject Author Date Answer Math Man 2017-05-08 12:25:33 No Subject broll 2015-06-05 23:25:21 Alternative Methodology K Sengupta 2008-08-18 12:26:33 Puzzle Solution K Sengupta 2007-10-23 05:31:11 re: Solution CORRECTED Ady TZIDON 2004-07-28 21:39:26 Solution Strahinja 2004-07-10 06:22:39 Squares, squares... Elisabeth 2004-06-28 19:36:09 re(2): solution Charlie 2004-06-26 00:19:07 re: solution ThoughtProvoker 2004-06-25 17:04:08 Just by hand Federico Kereki 2004-06-25 16:39:30 Message for Jim Captain Paradox 2004-06-25 16:17:13 a square jim 2004-06-25 11:52:01 Variations........ Penny 2004-06-25 11:18:56 solution Charlie 2004-06-25 09:55:56 Doing square roots by hand is a pain... Erik O. 2004-06-25 09:26:45

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