# More Puzzles

More Puzzles May 30, 2018

I’ve posted puzzles before (part 1, part 2) because of what they can teach us about how the human brain works. Spoiler: it works imperfectly.

You probably remember this puzzle:

A bat and a ball cost \$1.10 in total. The bat costs \$1.00 more than the ball. How much does the ball cost?

An answer will probably pop to mind—10 cents—but that’s wrong. (This and related puzzles were discussed in part 1.) Whether you give the intuitive answer or analyze further to find the correct answer says something about how you think. This is explored in an article provocatively titled, “3-Question Quiz Predicts Whether You Believe in God.”

Here are some more puzzles, just for fun (hints and answers are at the bottom).

#### Quick puzzles

1. “Jack is looking at Anne, and Anne is looking at George; Jack is married, George is not. Is a married person looking at an unmarried person?” Answers: (a) Yes, (b) No, (c) Not enough information. Source

2. Start with 100, then add 10% and then subtract 10%. How much do you have now?

3. Cup 1 holds milk, and cup 2 has an equal amount of coffee. Take a spoonful of milk from cup 1 and pour it into cup 2. Now take a spoonful from cup 2 and pour it into cup 1. Which cup is now more concentrated? Answers: (a) Cup 1 has a higher fraction of milk than cup 2 has coffee, (b) cup 2 has a higher fraction of coffee than cup 1 has milk, (c) the fractions are equal. Source

#### Puzzles about the real world

4. What happens to a helium balloon in a car when the car accelerates? Source

5. Why is a mirror left-right reversed? Why isn’t it top-down reversed, too?

6. Your canoe overturns, and you swim to shore. You’re looking for shelter, and it’s getting dark. Luckily, you find a cabin. Inside, there’s a box of matches and a kerosene lamp. While there is kerosene in the base of the lamp, the wick is too short to reach it. You’ve checked the cabin, and there’s no more kerosene or wicks. How do you light the lamp to signal for help?

#### Math puzzles

7. “Three people with different salaries need to find out their average salary without revealing individual salaries to each other. How?” Source

8. Three people rent a hotel room for \$60, so they each pay \$20. Later, the manager realized he charged too much—it was only supposed to be \$55. He sends a porter to the room with \$5. Each of the people keeps \$1, and they give the porter the remaining \$2 for a tip. So now each person has paid \$19 for the room (\$19×3 = \$57) and the porter got \$2. But they started with \$60, and \$57 + \$2 = \$59! Where is the other dollar? [I saw this one about 50 years ago.]

9. Joanne and her friends are seated around a large table. A dish with 25 cookies is pass around. Each person in turn takes a cookie and passes the dish along until it’s empty. The dish might go around once or several times, but the only rule is that the dish must start and end with Joanne (that is, she takes the first and last cookies). What are the possible values for the number of people sitting at the table? (h/t commenter Dave Gardner)

Whatever Nature has in store for mankind,
unpleasant as it may be,
men must accept,
for ignorance is never better than knowledge.
— Enrico Fermi

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