A monkey is composing a text consisting of random five-letter “words”. What is the smallest number of words in the text to guarantee that at least two of the words start with the same substring of length $3$?
2026-04-01 02:02:51.1775008971
Pigeon Hole Principle - How many words of length $5$ do you need to guarantee that at least two will start with the same string of length $3$.
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A good way to come up with the answer to a pigeonhole problem is to try, as hard as you can, to avoid the desired outcome. Maybe your first word starts with aaa, and then your next word starts with aab, and so on. How many words can you write before you are forced to repeat yourself? (You might find a smaller example useful for starters. How many words do you need to guarantee that at least two words start with the same letter? Or the same 2-letter string?)