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Problem 381

Combinatorics Difficulty 2.0 Find the answer UKMT Grey Kangaroo · United Kingdom · 2025

There were ten more truth-tellers than liars in a room. Everyone in the room was asked, “Are you a truth-teller?” and everyone gave an answer. A total of 20 people answered, “Yes.” How many liars were in the room?

(A) $0$ (B) $5$ (C) $15$ (D) $20$ (E) $25$

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