Each button in a box is big or small, and white or black. There is at least one big button, at least one small button, at least one white button, and at least one black button. Show that there are two buttons with different size and color.
Solution
Suppose not. There is a big button. Suppose it is white. Then the small button must be white also (or it would be have different size and color from the big white). Now if the black button is big it is different size and color from the small white. If it is small it is different size and color from the big white. Contradiction. We obtain an exactly similar contradiction if the big button is black.
© John Scholes
jscholes@kalva.demon.co.uk
1 Nov 2003
Last corrected/updated 1 Nov 03