Show that if you can turn G Y R B into a unicolor configurat

Show that if you can turn (G, Y, R, B) into a unicolor configuration, then three of these four numbers are equal modulo 4. Prove all your assertions

Solution

(G, Y, R, B) turn into a unicolor configuration if at least 3 of the given numbers have the same remainder when divided by 4.

For example: Consider we have 2 green, 2 yellow, 6 red, and 7 blue chameleons.

Then 2 mod 4 = 2

2 mod 4 = 2

6 mod 4 = 2

=> Three of these four numbers are equal modulo 4.

In this case, (G,Y,R,B) can turn into uni-color configuration.

Another example consider we have 6 green, 2 yellow, 10 red, and 7 blue chameleons.

Then 6 mod 4 = 2

2 mod 4 = 2

10 mod 4 = 2

=> Three of these four numbers are equal modulo 4.

In this case, (G,Y,R,B) can turn into uni-color configuration.