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### Discrete Reasoning Puzzles

These puzzles require sharp, logical thinking. Can you solve them?

## #21

A man is looking at a photograph of someone. His friend asks who it is. The man replies, "Brothers and sisters, I have none. But that man's father is my father's son." Who was in the photograph?

Solution

## #22

You have a 12 liter jug, an 8 liter jug, and a 5 liter jug. None of the jugs have any markings on them. The 12 liter jug is full, and the other two are empty. How can you divide the 12 liters of water equally (i.e., so two of the jugs have exactly 6 liters of water in them, and the third is empty)?

Solution

## #23

A gambler bet on a horse race, but the bookee wouldn't tell him the results of the race. The bookee gave clues as to how the five horses finished -- which may have included some ties -- and wouldn't pay the gambler off unless the gambler could determine how the five horses finished based on the following clues:

• Penuche Fudge finished before Near Miss and after Whispered Promises.
• Whispered Promises tied with Penuche Fudge if and only if Happy Go Lucky did not tie with Skipper's Gal.
• Penuche Fudge finished as many places after Skipper's Gal as Skipper's Gal finished after Whispered Promises if and only if Whispered Promises finished before Near Miss.

The gambler thought for a moment, then answered correctly. How did the five horses finish the race?

Solution

## #24

In a rectangular array of people, who will be taller: the tallest of the shortest people in each column, or the shortest of the tallest people in each row?

Solution

## #25

You have two cups, one containing orange juice and one containing and equal amount of lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in the orange juice or more orange juice in the lemonade?

Solution

## #26

All of my flowers except two are roses. All of my flowers except two are tulips. All of my flowers except two are daisies. How many flowers do I have?

Solution

## #27

Three humans and three monkeys (one big, two small) need to cross a river. But there is only one boat, and it can only hold two bodies (regardless of their size), and only the humans or the big monkey are strong enough to row the boat. Furthermore, the number of monkeys can never outnumber the number of humans on the same side of the river, or the monkeys will attack the humans. How can all six get across the river without anyone getting hurt?

Solution

## #28

A computer cable has seven connectors, arranged in a perfect circle -- so by rotating the plug, it can be connected to the outlet in any of seven different ways. Each of the connectors is numbered from one to seven, each number being used exactly once. The same is true for the holes in the outlet. The device that uses this cable only requires that one of the connectors match up to its corresponding hole in order to operate. How should you number the connectors on the plug and the holes in the outlet so that, no matter how the cable is rotated and plugged in, at least one connector matches up?

Solution

## #29

Five men and five dogs (each man owned a dog) went hiking. They encountered a river that was swift and deep. The only way to cross it was an abandoned boat, left ashore on their side. But it would only hold three living things. Unfortunately, the dogs were edgy and could not be near another person (not even momentarily) unless its owner was present. One of the dogs attended a highly advanced, highly specialized obedience school and therefore knew how to operate the boat -- the other dogs lack this skill. How did the five men and the five dogs cross the river?

Solution

## #30

On your travels, three men stand at a fork in the road. You're not sure which fork you need to take, but each of the three men do. One of these people tells the truth, one always lies, and the third tells the truth sometimes and lies the other times. Each of the three men know each of the others, but you don't know who is who. If you could ask only one of the men (chosen at random, since you don't know which man is which) one yes/no question, what question would you ask to determine the road you wish to take?

Solution