12 More Puzzles

12 More Puzzles December 28, 2020

I recently explored a specific kind of puzzle in “Counterintuitive Puzzles that Should Be Easy.” I’ve explored other puzzles to shed some light on the religion question: the Monty Hall problem and the Puzzle of the Hidden Dots. There is more to be said about the odd ways the human brain works, but let’s postpone that and simply enjoy a few more puzzles for their own sake this time.

Write your answers to the puzzles that were new to you and check them with the answers below.

Got any good puzzles that you use to stump your friends? Tell us about them in the comments.

Quick ones

Let’s start with some quick ones like those in the previous post. See if the intuitive answer is correct.

1. If fence posts are put in every 7 feet, how many posts are needed to make a fence 77 feet long?

2. If it takes a chiming clock 3 seconds to strike 6:00, how long does it take to strike midnight? Ignore the duration of the sound of each chime. (h/t commenter Richard S. Russell)

Word sense

3. An online parser can make sense out of the following sentences. Can you?

Here’s an example of a confusing sentence: “While Anna dressed the baby played in the crib.” That probably sounds odd until you mentally punctuate it like this: “While Anna dressed, the baby played in the crib.” Now try these:

  • The old man the boat.
  • While the man hunted the deer ran into the woods.
  • I convinced her children are noisy.
  • The coach smiled at the player tossed the Frisbee.
  • The cotton clothes are made up of grows in Mississippi.
  • The horse raced past the barn fell.

Easy physics puzzles

These are physics versions of the puzzles that should be easy to answer.

4. Where does the length of a year come from?

5. Why is it colder in the winter?

6. A rowboat is floating in a swimming pool. Inside the rowboat is a cannonball. Take the cannonball and drop it overboard. Does the water level on the side of the pool rise, fall, or stay the same?

Something must be wrong here

7. A friend of mine was from Iowa, and he said that there was quite a rivalry with the neighboring state of Missouri. Jokes were told in Iowa about how stupid Missourians were. They claimed that if Iowa gave those counties that bordered on Missouri to Missouri, it would raise the IQ of both states.

But wait a minute—there has to be something wrong with that. Both states can’t improve, right?

8. Proof that 1 = 2

  • Let a = b
  • Multiply both sides by a:

a2 = ab

  • Subtract b2 from each side:

a2 – b2 = ab – b2

  • Factor both sides:

(a – b)(a + b) = b(a – b)

  • Cancel (a – b) from both sides:

a + b = b

  • Substitute (remember that a = b):

a + a = a

  • Collect:

2a = a

  • Divide by a:

2 = 1 (But something has to be wrong here—what is it?)

Increasingly difficult puzzles

9. You’re in the middle of an island covered uniformly with a dense, dry forest. Lightning sets the north end of the forest on fire, and the wind is blowing to the south. The coast is cliffs all around, so you can’t jump into the water to wait out the fire. The fire will reach you in an hour, and all you have is a backpack with things typically taken on a hike. What can you do to save yourself?

10. You and I are going to meet at a cafe. The server delivers a coffee with milk on the side just as I get a text from you saying you will be 15 minutes late. Being the polite person that I am, I want to wait for you before drinking my coffee. If I want it to be as hot as possible, do I pour the milk in now or wait until you get here?

11. Suppose we have 6-sided dice that don’t have the usual numbers 1 through 6 on them. If my die has a 6 on every face and yours has a 5 on every face, we could roll our respective die and I would beat you every time. Now suppose I change to a die with faces {6, 6, 6, 6, 1, 1}. My die is still the better one, but now I would beat your all-5s die only 2/3 of the time. It’s easy to imagine die A being better than B, and B being better than C, but the puzzle is to make this loop around. That is, create dice such that A beats B, B beats C, and C beats A.

12. Does the balance tip to the right, tip to the left, or remain unchanged?

Click on the Continue below for hints and then answers.

Everyone is entitled to their own opinion
but not their own facts.
— Daniel Patrick Moynihan


(This is an update of a post that originally appeared 7/21/16.)

Image from stevepb (free-use license)


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