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6 indistinguishable coins, 2 false May Olympiad (Olimpiada de Mayo) 2015 L2 P2

Source:

September 26, 2021
combinatoricsweight

Problem Statement

66 indistinguishable coins are given, 44 are authentic, all of the same weight, and 22 are false, one is more light than the real ones and the other one, heavier than the real ones. The two false ones together weigh same as two authentic coins. Find two authentic coins using a balance scale twice only by two plates, no weights.
Clarification: A two-pan scale only reports if the left pan weighs more, equal or less that right.