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One Question About Four Stones

We just solved the problem of one question to determine one of three objects. Let's make one step further now.
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An honest man has four stones – white, light gray, dark gray, and black.

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

Can you determine which stone the man chose?

Dmitri Papichev
Thursday, June 16, 2005

If I choose 2 stones out of the three you didn't choose, will it be darker than the one you have?

Yes : White
No : Black
Dont know : light grey
Illegal Question : Dark grey!!!!

saai ananth S.S.
Friday, June 17, 2005

Please elaborate.
I don't see how the answers for dark gray and light gray would fall in the different categories.

Dmitri Papichev
Friday, June 17, 2005

If I choose a stone which is not yours, and not exactly one shade darker than yours, will it be darker than the stone exactly one shade darker than yours?

White: yes
LightGray: don't know
Dark Grey: no
Black: illegal question

WanFactory
Friday, June 17, 2005

Nice solution, WanFactory!

It is much more elegant than mine own. I was thinking along the lines of counting the stones from 0 to 3, and then applying some mathematical tricks like referring not to the values, but to the logarithms of the values :)

Dmitri Papichev
Friday, June 17, 2005

Unfortunately, it's not possible to edit your own posts here.

Dmitri Papichev
Friday, June 17, 2005

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