Solution
Look at two adjacent rows, A and B. Suppose row A has
• r red dots beside red dots in B,
• b blue dots beside blue dots in B,
• u red dots beside blue dots in B and
• v blue dots beside red dots in B.
Then there are r red and b blue segments joining elements of A to elements of B.
A has r + u red dots and b + v blue dots, while B has r + v red dots and b + u blue dots. We get
that r+u = b+v and r+v = b+u. Rearranging, we get r−b = v −u = −(v −u); in other words,
r − b = 0, or r = b.
Hence between adjacent rows, the number of red segments equals the number of blue segments.
The same is true for adjacent columns. Thus the total number of blue segments is equal to the
total number of red segments, as desired.
solution does not belong to me..I saw already in forum...i like it so I added to my archive..Thanks to the person who solved...