Find the four digit number? Find a four digit number which is an exact square such that the first two digits are the same and also its last two digits are also the same.

The Number is of the form 1000A + 100A + 10B + B = 11( 100A + B ) = 11 ( 99A + A + B )
Since it is a perfect square number , (99A + A + B) should be divisible by 11 hence (A + B) is divisible by 11....(i)
Any perfect square has either the digits 1 , 4 , 9 , 6 , 5 , 0 at the units' place , ...(ii)
Only numbers which satisfy property i and ii are enlisted:
7744
2299
5566
6655
[Note that (A + B) being divisible by 11 was a crucial property to note]
Clearly , Only 7744 is a perfect square number.
