AMC / AIME · Pigeonhole Principle · Medium

Pigeonhole Principle: What is the minimum number of people needed to guarantee that four share a birth month?

Forced collisions.

Try the problem

What is the minimum number of people needed to **guarantee** that **four** share a birth month?

Hint and answer

Concept to use

Strong form.

Hint

At most 33 per month → 3⋅12+13\cdot12+1.

Answer

37

More Pigeonhole Principle problems

Practice more with the free Pigeonhole Principle worksheet generator, or browse the full problem library.