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### Discrete Reasoning Puzzles

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

## #41

Three people go fishing -- two fathers and two sons. How is this possible?

Solution

## #42

Mr. Slow, Mr. Medium, Mr. Fast, and Mr. Speed must cross a rickety rope bridge in 17 minutes. The bridge can carry at most two people at a time. Furthermore, it's dark, and there is only one flashlight; any single person or pair of people crossing the bridge must have the flashlight with them. (The bridge is too wide for the flashlight to be thrown; it must be carried across.)

Each man walks at a different speed. A pair travelling together must walk at the rate of the slower man. Mr. Slow can cross the bridge in at most 10 minutes; Mr. Medium can cross in 5 minutes; Mr. Fast can cross in 2 minutes; Mr. Speed can cross in 1 minute. How do all four men get across in the bridge in 17 minutes?

Solution

## #43

You have twelve marbles. Eleven of the marbles are of equal weight, but one is heavier or lighter. You have a balancing scale you can use to find this marble and figure out if it weighs more or less than the others. What is the minimum number of weighings required to do this?

Solution

## #44

You have two slow-burning fuses, each of which will burn up in exactly one hour. They are not necessarily of the same length and width as each other, nor even necessarily of uniform width, so you can't measure a half hour by noting when one fuse is half burned. Using these two fuses, how can you measure 45 minutes?

Solution

## #45

You have an eight-gallon tank of water, which is completely full, an empty five-gallon tank, and an empty three-gallon tank. Without throwing any water away, can you put exactly four gallons in the eight-gallon tank and four gallons in the five-gallon tank?

Solution

## #46

Five competitors -- A, B, C, D, and E -- enter a swimming race that awards gold, silver, and bronze medals to the first three to complete it. Each of the following compound statements about the race is false, although one of the two clauses in each may be true.

• A didn't win the gold, and B didn't win the silver.
• D didn't win the silver, and E didn't win the bronze.
• C won a medal, and D didn't.
• A won a medal, and C didn't.
• D and E both won medals.

Who won each of the medals?

Solution

## #47

Two days ago, Suzy was 8. Next year, she'll be 11. How is this possible?

Solution

## #48

A man leaves home for a mountain at 1pm and reaches the top at 3pm. The following day he departs from the top at 1pm and gets home at 3pm, by following the same path as the day before. Was he necessarily ever at the same point on the path at the same time on both days?

Solution