perplexus.info :: Liars and Knights : Donuts

Donuts (Posted on 2007-11-05)

Friends Tom, Dick and Harry are each either a knight, always telling the truth, or a liar, always lying. One day they went to the donut shop and bought six donuts.

Tom claimed to have gotten only one donut, while Dick claimed Tom had two. Harry said Tom had more than three.

All three agreed that Dick had two donuts.

If each of the three got at least one donut and no donuts were shared or divided, how many donuts did each friend get?

Submitted by Charlie

Rating: 4.0000 (3 votes)

Solution: (Hide)

As each had a different statement about the number that Tom had, at most one could be a knight. But since they agreed on Dick's donut count, they must all be the same type, meaning that all three are liars.
Since all are liars, Tom must have had exactly three donuts, leaving three for Dick and Harry. Thus one of those two got one and the other got two. Dick couldn't have gotten two as that was what all the liars said he had. So Dick had one donut and Harry had two.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Sol	Andre	2010-05-24 19:06:43
solution	Dave	2007-11-06 06:02:35
Solution	K Sengupta	2007-11-06 04:07:56
Solution by Brute Force	Vernon Lewis	2007-11-06 03:55:55
Solution	Brian Smith	2007-11-05 11:46:38
Solution	Dej Mar	2007-11-05 10:31:03

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