MathDiscrete mathCombinatorics

The pigeonhole principle

Vasily and the blackboard

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Vasily writes some numbers on the blackboard. He wants to write 55 different two-digit numbers on the blackboard, so that there are no two that add up to 100. Can he do this?

Tip: Divide all numbers from 10 to 90 (except 50) into pairs.

Select one option from the list

Yes, he can do this.

There are no two-digit numbers that add up to 100.

The pigeonhole principle can't be applied to this problem.

No, he can't do this.

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