# Colours

• May 4th 2009, 12:17 AM
Aquafina
Colours
• May 4th 2009, 01:26 AM
bebrave
• May 4th 2009, 03:13 AM
Aquafina
how does this help me? sorry i didnt understand that
• May 4th 2009, 03:44 AM
bebrave
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...
• May 4th 2009, 03:54 AM
Aquafina
doesnt it look like this?
• May 4th 2009, 04:00 AM
bebrave
yeah
shape like this
blue---blue,red---red
red---red,blue---blue
blue---blue,red---red
red---red,blue---blue
• May 4th 2009, 04:03 AM
Aquafina
but in this one each time the colour on a row is alternate to the previous one, in yours they are at random order?