Do you often go with your instincts when a new situation arises? Or do you
follow a deliberate strategy?

The Cognitive Reflection Test: Puzzle #8

The total cost of a ball and a bat is $1.10. A dollar more goes toward the
bat than the ball. What is the cost of the ball?

How long would it take 100 machines to produce 100 widgets if 5 machines
took 5 minutes to produce 5 widgets?

There is a lily pad patch in a lake. The patch doubles in size each day.
How long would it take for the patch to cover half of the lake if it takes
48 days to cover the entire lake?

These inquiries are taken directly from a
Shane Frederick
study article.

Do you frequently rely on your gut feelings when solving a new problem? Or
do you want to go cautiously and methodically? The Cognitive Reflection Test
was developed to assess people's propensities for using one or the other of
these two cognitive modes, which everyone utilizes in some combination
throughout their life. You could have relied on your intuition if the
solutions appeared easy to you right away but, in reality, these riddles
call for a bit more thought than one might anticipate. See if any of your
responses alter by giving them another, slower pass.

Next Monday, we'll publish a new problem along with the answer. Do you know
of a challenging puzzle I should discuss here? My email address is
gizmodopuzzle@gmail.com.

Gecko Trek Solution to Puzzle #7

This week's shout-out goes to reader Dr. Emilio Lizardo for being the first
to post the right answer, despite the fact that many of you thought of
creative ways to get around the question, such as having the gecko construct
a teleportation device or pointing out that a large enough gecko would
already be touching the other corner of the room.

Only 22.36 feet, or 10 times the square root of 5, are required for the
gecko to complete its crawl. The number alone doesn't reveal too much. How
do we get there? We are aware that on flat terrain, a straight line connects
any two places. Our issue is that the cubic room's faces do not form a
smooth surface. We unfold the cube and flatten it to correct this.

Keep in mind that the red dot designates the room's diagonally opposite
corner if the gecko starts off on the diagram's right-hand side. Our cubic
room is now neatly mapped into a flat surface. The shortest distance is
covered by taking a direct line between these places. From here, the
Pythagorean theorem takes us home. The hypotenuse of a right triangle with
sides measuring 10 and 20 is the route. We obtain c2 = 102 + 202 by labeling
the hypotenuse's length as c.

Our solution is obtained by solving the previous equation for c.

A net is the name for the unfolded diagram of a cube or other 3D form. Nets
are useful for a variety of issues concerning the shortest distance on a
solid's surface. The key to the Gecko Trek mystery is to even consider using
a net; once you do, the rest quickly becomes clear. Knowing how to utilize a
net is just the beginning for future problems because solids may be unfolded
in a variety of ways! I offer the infamous
spider and fly puzzle
as a challenging illustration. There is a spoiler in that link. If you want
to try the puzzle on your own, keep your eyes closed because the article's
image reveals the solution.