Mathemagical Trick Indeed

Probability Level 1

A magician wants to show a "mathemagical" trick in front of a group of young kids. He declares, "I bet that there are at least 2 of you who have the same birth month. Isn't that amazing?"

What is the minimum number of kids sitting in front of him that guarantees him to pull off this trick?

The answer is 13.

2 solutions

Sam Bealing
Jul 25, 2016

Relevant wiki: Pigeonhole Principle

As there are $12$ months, selecting $12$ toddlers won't work because they could all have birthdays in different months but by pigeon hole principle $13$ toddlers can't have birthdays in the same month so the answer is:

$\boxed{\boxed{13 \text{ toddlers}}}$

Anandmay Patel
Aug 5, 2016

Solution through use of simple pigeon hole principle.

How? $\quad$ $\quad$

Pi Han Goh - 4 years, 10 months ago

Pigeon hole principle:If n pigeons are put into n-1 pigeon holes,then one cannot avoid putting 2 pigeons in the same pigeon hole. Similarly,if there are 13 children to be put their month of birth in (13-1) months,it is not possible to avoid putting 2 children's birth date in the same month. But,it is possible to do so if there are 12 children.SO answer to the question is 13(least no. of children.)

Anandmay Patel - 4 years, 10 months ago

Mathemagical Trick Indeed

The answer is 13.

2 solutions

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