solve it up!

If we put aabb as a^2 and b^2 then we find combination of a and b that a+b is 11 where 4 digit number is perfect square as well. K.K.GARG,India

i solved it by programming in Vb 2013 ....

Private Sub Button1_Click

Dim x As Single

Dim a, b, c, d As Single

For i = 32 To 99

       x = i * i

        a = x Mod 10

        b = x Mod 100 - a

        c = x Mod 1000 - a - b

        d = x Mod 10000 - a - b - c

        If (a = b / 10 And c = d / 10) Then

            Label1.Text = a+c/100

        End If

 Next

End Sub

The result is 11 ... So Easy :D

The four digit number is 1000a+100a+10b+b =1100a+11b =11*(100a+b) So 11 must be a factor of 100a+b. This criteria is satisfied by the set of (a,b)=(2,9), (3,8) etc.. and a+b is always equal to 11. Consequently a=7 and b=4 gives 7744 which is a perfect square.

a a b b=7744, where a=7 and b= 4 therefore a+b=11