# How to prove that there is a string of consecutive days in which a factory produces exactly $15$ tables

The problem is about "Generalized Pigeonhole Principle" from the Combinatorics textbook, and I really don't know how to solve it. The following problem was translated from Thai into English.

The factory wants to produce $44$ tables in $30$ days, each day must produce at least $1$ table. Prove that there must be a string of some number of consecutive days in which this factory produces exactly $15$ tables.

In my textbook, there is also a hint said