## Chacham's Journal: Puzzle: Section I: Paradoxes and dilemmas 2

Just scanned this in, and needed only a little fixing.

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Chapter 16 LOGICAL PUZZLES

A logical puzzle requires to a special degree the "flash of insight" that is characteristic of all intellectual problem-solving. The solution is easy provided one gets the point, but the point is likely to be elusive and is often intentionally made more so by the way the puzzle is stated.

Section I: Paradoxes and dilemmas

1. THE HOTEL BILL

Three men shared a hotel room, and each paid ten dollars to the cashier in advance. Later the cashier discovered that the total charge should have been twenty-five dollars instead of thirty, and he gave five dollars to the bellboy with instructions to refund it to the guests. The bellboy in fact refunded only one dollar to each of the three and kept two dollars for himself. Thus each of the men paid nine dollars for the room, a total of twenty-seven dollars. This amount added to the two dollars that the bellboy kept is only twenty-nine dollars. What happened to the other dollar?

2. YOUR MONEY AND MINE

I make this proposition to you: "You take all the money that you have on your person and pile it on the table, and I will do the same. Then whichever of us shows the smaller amount will take it all. The odds are in your favor because you have an exactly even chance of winning, and the amount that you have a chance of winning is greater than the one that you have a chance of losing." Is this correct?

3. TOSSING THREE COINS

Is this reasoning sound? When three coins are tossed at the same time, the chances are even that

all will be heads or all tails; two of the three will always be the same, either both heads or both tails; and the third coin is just as likely to be heads as tails, and hence just as likely to match the other two as not.

4. THE BEAR HUNTER

A hunter sat down to rest and was startled at being nudged by a bear. The hunter took to his heels and ran straight north for a distance of 200 yards. The bear, being just as frightened as the hunter, also ran, going straight east for a distance of 200 yards. After his run the hunter regained his nerve, aimed his gun straight south, and killed the bear. What color was the bear?

5. THE RAISE

A man who had asked his employer for a raise in salary was told: "Why, you work only eight hours each day, which is just one-third of the day, or 122 days in a year of 366 days. If you deduct 104 days for the Saturdays and Sundays on which you do not work, that leaves only 18 days, and these 18 days are just equal to the four holidays and your two-weeks vacation. This brings the total down to zero, so that in fact you do not work for me at all. Why should I give you a raise?" What is wrong with the employer's statement?

6. THE MARKSMEN

Jim and Bill engaged in a rifle-shooting contest, comparing their success in hitting a small target from a considerable distance. They took fifty shots each and made the same number of hits, twenty-five. After taking time out for a drink, they resumed their shooting. They were not as good this time, for Jim got only three hits in thirty-four shots, while Bill got no hits at all in twenty-five shots. Since Jim's record after the drink was better than Bill's, and since his record before the drink was just as good, Jim's record for the day was clearly better than Bill's. Or was it?

7. THE FIRST CASE

John Lawyer borrowed five hundred dollars from Mr. Jones, his father-in-law, to help finance his legal education, agreeing to repay the loan as soon as he had won his first case. After he secured his degree, John was slow at beginning practice and Mr. Jones sued him for the money. Mr. Jones said, "If I win the suit I will collect the money; if I lose the suit, John will have won his first case and must pay me according to the terms of our agreement, and so I cannot lose." On the other hand John argued, "If I win the suit I will not have to pay, but if I lose the suit I will not have won my first case, and still will not have to pay, according to the agreement." How can these arguments be reconciled?

8. WHO SHAVES THE BARBER7

In a certain community the only barber shaves all the men who do not shave themselves. That is, every man either shaves himself or is shaved by the barber, and no man does both. The question is,

who shaves the barber?

## The barber paradox... (Score:2)

Russell's Paradox [wolfram.com]

## Laconic Answers (Score:2)

2. No.

3. No.

4. White.

5. Double-counts after-hours part of weekends & holidays.

6. Not clearly.

7. J. Lawyer represents Mr Jones; Mr Jones represents J. Lawyer.

8. No such community exists.