Track / Stage 4 / 228 of 340 #488 of 1964

Problem 488

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

A translation office translates from English, German, and Russian. Among those who know the individual languages, there are 1, 2, and 3 fewer people who know multiple languages. One person speaks all three languages, and 8 people only know one foreign language. How many people work at the office?

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Official solution

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.