September 2024
Problem of the Month

Tom, Dick, and Harry
Submitted by K. Sengupta of Calcutta, India

Friends Tom, Dick and Harry are each either a truthteller, 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?

Solution:

Tom had 3 donuts, Harry had 2 donuts, and Dick had 1 donut.

As each had a different statement about the number that Tom had, at most one could be a truthteller.
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.

Correctly solved by:

1. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
2. Davit Banana	Istanbul, Turkey
3. Kamal Lohia	Holy Angel School, Hisar, Haryana, India
4. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
5. Kelly Stubblefield	Mobile, Alabama, USA
6. Ryan Hall	Parkview Elementary, Chico, California, USA

Send any comments or questions to: David Pleacher