ABC and CBA are two three-digit decimal numbers, with A and C different non-zero digits. Squares of these numbers are five-digit numbers DEFGH and HGFED respectively. Find all such three-digit numbers.
The problem is symmetrical in A and C so let's look for A>C. That'll give us half the solutions and swapping A and C the other half.
For A>=4 the square of ABC is 6-digits so (A,C) is limited to (3,1), (3,2), (2,1).
For (3,1) ABC=301, 311 are solutions.
For (3,2) there are no solutions.
For (2,1) ABC=201, 211, 221 are solutions.
So the set of solutions is 102,103,112,113,122,201,211,221,301,311.
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Posted by xdog
on 2013-02-13 00:14:32 |
Confirming solutions
