This week’s puzzle (three really small puzzles) is best solved without an introduction. I’ll explain why after I give it a shot.

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

**Puzzle #8: Cognitive reflection test**

- The total cost of the bat and ball is $1.10. A bat costs $1.00 more than a ball. How much does the ball cost?
- If it takes 5 machines 5 minutes to make 5 widgets, how long will it take 100 machines to make 100 widgets?
- In a lake, there is a patch of lily leaves. Every day, the patch doubles in size. If the patch takes 48 days to cover the entire lake, how long will it take for the patch to cover half of the lake?

These questions are taken directly 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? Everyone uses a combination of these two cognitive modes in their lives, and the test of cognitive reflection is designed to measure people’s tendencies toward one or the other. If the answers seem immediately obvious to you, you may be relying on your intuitive thinking, when in reality these riddles require more thought than one might expect. Give them another, slower pass and see if any of your answers change.

We will post the solution next Monday with a new puzzle. Do you know of a cool mystery I have to cover here? Send it to me: [email protected]

**Solve Puzzle #7: Gecko Trek**

While many of you have come up with clever ways to dodge the question like having your gecko build a teleportation device or noticing that a large enough gecko is already touching the opposite corner of the room, this week the shout out goes to the reader **Dr. Emilio Lizardo** For being the first to post the correct answer.

A gecko should only crawl about 22.36 feet, or 10 times the square root of 5 (10 x sqrt (5)) feet. The number alone doesn’t shine much. How do we get there? 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 do not form a flat surface. To correct this, we unfold the cube and flatten it!

Note that if the gecko originates on the right side of the diagram, the red dot indicates the diagonally opposite corner of the room. Now we have a flat surface that cleanly maps the cubic room. The path of a straight line 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. By naming the hypotenuse length c, we get c^{2} = 10^{2} +20^{2}.

c’s solution above to get our answer.

An unfolded diagram of a cube or other three-dimensional shape is called a *network*. Meshes are useful for all kinds 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 just pops up quickly. For other puzzles, knowing how to use the grid is only the first step, because solids can unfold in many different ways! Oldest celebrity Spider and fly problem As a deceitful example. Spoiler alert at this link. The photo in the article gives the answer, so blink your eyes if you want to try the puzzle yourself.

“Typical beer trailblazer. Hipster-friendly web buff. Certified alcohol fanatic. Internetaholic. Infuriatingly humble zombie lover.”