Simple puzzles can give insight into how our brains work.

Our brains don’t work as well as we might think. We have a poor intuitive grasp of probability (more here and here). We also have lots of inherent biases. For example: new information to correct a misperception can backfire (more here and here), cementing a false belief more strongly. And our memories are unreliable (more here and here).

3 easy puzzles

These puzzles were designed to reveal how our brains are fallible. Write your answers so you can check them below. First, some very easy ones.

1. 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?

2. If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

3. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

These questions don’t take a lot of thought. Indeed, an intuitive answer pops instantly to mind for some people. How confident are you in your answers?

3 more, about as easy

4. If you’re running a race and you pass the person in second place, what place are you in?

5. A farmer had 15 sheep and all but 8 died. How many are left?

6. Emily’s father has three daughters. The first two are named April and May. What is the third daughter’s name?

The last 3, slightly harder

These last three require more thought.

7. “You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?”

8. You have a rope around an earth-sized sphere at the equator. That makes it about 40,075,160 meters in length. Now you increase the rope length by 10 meters uniformly around the globe so that it’s suspended over the surface equally. What is the gap between the surface of the sphere and the rope?

9. You have 100 pounds of potatoes, which are 99% water by weight. You let them dehydrate until they’re 98% water. Now how much do they weigh?

(This is an update of a post that originally appeared 7/6/16.)

Image from hans-juergen (license CC BY-ND 2.0)

Answers on the next page: