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One Question About Three Tokens

An honest man has three tokens – white, gray, and black.

He secretly chose one of the tokens, and allows you to ask him one question, which he can answer “Yes”, “No”, or “I don’t know” (the questions assuming other possible answers are not allowed).

Can you determine which token the man chose?

Dmitri Papichev
Tuesday, June 14, 2005

Hmm... So the trick is to get three unique answers for the three different stones.

How about:
"In my closed fist I have a gray stone of my own.
Is the stone you chose darker than mine?"

Answer:
Black: Yes
White: No
Gray: I don't know

Hmm... the only other ones I can think of are similar shade-comparing questions. Any other class of question you can think of?

BradC
Wednesday, June 15, 2005

We consider gray as a distinct color, not a range of colors. So the answer in case of the gray token chosen will be "No" - the same as in case of the black token.

Thus, we need some other question.

Dmitri Papichev
Wednesday, June 15, 2005

If I chose a stone that you did not pick, would my stone be darker than yours?

black: no
white: yes
gray: I dont know

WanFactory
Wednesday, June 15, 2005

Solved! :)

Dmitri Papichev
Thursday, June 16, 2005

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