It sounds like an interesting group of people…
The trick to thinking about this puzzle is understanding that it’s not asking how many people speak three languages — there’s no way to know — but rather what the minimum number is.
I found it easier to think about this puzzle using a smaller number of people. What if we had 10 people, 9 of whom could speak Spanish, 8 of whom could speak French and 7 of whom could speak English?
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We’ll number them 1 to 10. Let’s start by assuming that guests 1 through 9 speak Spanish. It doesn’t matter who we choose since they were randomly numbered. Now, if we want as little overlap as possible, we can have guests 3 through 10 speaking French. That leaves us with people 1, 2 and 10 who only speak one language so far.
If we want to minimize the number of trilingual people, the people who only speak one language so far need to become bilingual. That leaves 4 (7-3) of the English speakers who must also speak French and Spanish.
Now we can scale that logic up to 100 people. If the first 90 speak Spanish, and the last 80 speak French, that leaves 30 people who only speak one language to overlap with. Thus, there are 45 (75-30) trilingual guests at the party.
The puzzle was adapted from one by Sharp Brains.
