83% of People Got at Least One Question Wrong on This Psychology Test

It’s best to solve this week’s puzzle (really, three mini-puzzles) without an introduction. I’ll explain why after you’ve given it a shot.

Did you miss last week’s puzzle? Check it out here, and find its solution at the bottom of today’s article. Be careful not to read too far ahead if you’re still working on that puzzle!

Puzzle #8: The Cognitive Reflection Test

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 are directly quoted from a research paper by Shane Frederick.

Do you tend to follow your gut instinct when faced with a new problem? Or are you more likely to take a slow, methodical approach? Everybody uses some mix of these two cognitive modes in their lives, and The Cognitive Reflection Test was designed to measure people’s tendencies toward one or the other. If the answers seemed immediately obvious to you, you may have been relying on your intuitive thinking, when in fact these puzzles require a little more reflection than one might expect. Give them another slower pass and see if any of your answers change.

We will post the solution next Monday along with a new puzzle. Do you know a great puzzle that I should cover here? Send it to me: [email protected]

Solution to Puzzle #7: Gecko Trek

While many of you came up with clever ways to dodge the question like having the gecko build a teleportation device or noting that a sufficiently large gecko would already be touching the opposite corner of the room, the shout-out this week goes to reader Dr Emilio Lizardo for being the first to post the correct answer.

The gecko only has to crawl about 22.36 feet, or 10 times the square root of 5 (10 x sqrt(5)) feet. The number alone doesn’t illuminate much. How do we arrive at it? We know that on flat surfaces, the shortest distance between two points is a straight line. Our problem is that the faces of the cubic room don’t form a flat surface. To rectify this, we unfold the cube and flatten it out!

Notice that if the gecko originates on the right-hand side of the diagram, then the red dot signifies the diagonally opposite corner of the room. Now we have a flat surface that cleanly maps onto our cubic room. The straight-line path connecting these points achieves the shortest distance. The Pythagorean theorem carries us home from here. The path is the hypotenuse of a right triangle with side lengths 10 and 20. Labeling the length of the hypotenuse c, we get c² = 10² + 20².

Solving the above for c yields our answer.

The unfolded diagram of a cube or other 3D shape is called a net. Nets come in handy for all sorts of problems involving the shortest distance on the surface of a solid. The crux of the Gecko Trek puzzle is to think of using a net at all, and the rest dawns swiftly. For other puzzles, knowing to use a net is only the first step, because solids can be unfolded in many different ways! I submit the famous spider and the fly problem as a tricky example. Spoiler alert on that link. The image in the article gives away the answer, so blur your eyes if you’d like to attempt the puzzle on your own.