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
For $i$ = $1, 2, 3, ... , 28$ , then $x$$i$ is the value of tables produced from first day to the $i$th day.
Can you help me?