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#1069243 - Wed Oct 15 2014 06:03 AM Alice
baldhair Offline
Explorer

Registered: Tue Aug 05 2014
Posts: 81
Loc: Gloucestershire UK
My young sister Alice is a very bright girl indeed. It was her birthday recently, and the family gave a party. We played lots of party games, including one devised by myself that I thought Alice would like. We have two cousins named John and Jane. I took them aside and gave them their instructions. We agreed that one of them should play the role of a liar and answer all questions falsely, and the other should play a truth-teller and answer all questions truthfully. One of the two was to hold a coin in a clenched fist, the other to hold up an empty clenched fist. We then explained the situation to Alice and the guests, though not saying which one was the liar. They had to determine which one held the coin, but could ask only one question. It was Alice (of course) who asked the clever question. She said to John: "Does the liar have the coin?" John answered "Yes".

Now, was John lying, or was he telling the truth? Or is it impossible to tell? And which one has the coin? Or can't we tell?

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#1069253 - Wed Oct 15 2014 07:48 AM Re: Alice
deputygary Offline
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Registered: Thu May 24 2007
Posts: 283
Loc: South Dakota USA
Jane has the coin.
1) If John was a liar and he had the coin he'd say "No".
2) If John was a truth-teller and had the coin he'd say "No".
3) If John was a liar and Jane had the coin he'd say "Yes".
4) If John was a truth-teller and Jane had the coin he'd say "Yes".
Since he said "yes" then either 3 or 4 is correct and we'd don't care which one is because the result is that Jane has the coin.
_________________________
"When you argue for your limitations, they become yours."--Richard Bach, Illusions

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#1069513 - Fri Oct 17 2014 02:00 AM Re: Alice
baldhair Offline
Explorer

Registered: Tue Aug 05 2014
Posts: 81
Loc: Gloucestershire UK
Yes, Gary, well-reasoned. My reasoning was slightly different, but the result was the same. The trouble with these little exercises is that the first correct solution prevents others having a go. If anyone is sufficiently interested, suggestions might help.

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