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 donīt 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?
Your answer that the first and second woman both must have 2's is correct as is your determination as to when they realize this. (A realizes she has a 2 when B does not know her own number at the first turn and B realizes that she must have a 2 when C does not know her number at her first turn).
There is only one remark that you make that I question. You state that C is the last to know her number. In fact, C knows she must have a 2 or a 3, but she never has sufficient information to distinguish which one.
Gordon S.
Response to Gadsen
