Answer to Question #256967 in Discrete Mathematics for htd

Question

Show, by giving a proof by contradiction, that if 100 balls are placed in nine boxes, some box contains 12 or more balls. 

Answer 1

Let each box contain less than 12 balls (maximum 11).

Then the maximum number of balls is $11 \cdot 9 = 99$, which contradicts the condition of the question.