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In triangle △ABC, the reflection of its incenter over side AB is its circumcenter.

Find the measure of ∠C in degrees.
(No Solution Yet, 0 Comments) Submitted on 2019-12-06 by Danish Ahmed Khan   
Difficulty: 3 of 5 Bonus: Three women, three numbers (in Logic) Rating: 3.38
Three women were seated around a table. After blindfolded, a numbered disc was pasted on each of their foreheads. The women were truthfully told "Each of you has either a 1, a 2 or a 3 on your forehead, and the sum of your numbers is either 6 or 7".

After the blindfolds were removed, each woman in turn was asked to name the number on her forehead without seeing it. The question was repeated until only one woman failed to name the number on her forehead.

When it was logically possible to name the number on her forehead, each woman did so; when it was not logically possible to name the number on her forehead, she would said "I dont know my number", and waited until the question was repeated to her next time around.

Each woman had a 2 on her forehead. Which woman failed to name her number?

(Solution Posted, 27 Comments) Submitted on 2005-12-15 by pcbouhid   
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