Suppose that 25 days are chosen at random from a calendar. Explain why at least 3 of the 25 days must lie in the same month. Do some research to find the name of the principle you've used, and clearly describe it in your own words.

There are 12 months in a year, if we chose 25 random dates we'll have two dates per month

2x12=24

and one extra day that will fit in another month.

The principle used for this kind of problem is the pigeonhole principle, supposing we have a number k of pigeonholes and n pigeons to be placed in them, If the number of pigeons is bigger than the pigeonholes, there will be at least one pigeonhole with more than one pigeon.

This happens with our problem, 25 days is a larger number than 12 months two times (24), this means we'll choose at least one month three times.

I hope you find this information useful! good luck!