Slitherlink

https://commons.wikimedia.org/wiki/File:SurizaL%C3%B6sung.png
Image: Wikimedia Commons

In this original logic puzzle by the Japanese publisher Nikoli, the goal is to connect lattice points to draw a closed loop so that each number in the grid denotes the number of sides on which the finished loop bounds its cell, as above: Each cell bearing a “1” is bounded on 1 side, a “2” on 2 sides, and so on.

Here’s a moderately difficult puzzle. Can you solve it? (A loop that merely touches a cell’s corner point without passing along any side is not considered to bound it.)

https://commons.wikimedia.org/wiki/File:Slitherlink-example.png
Image: Wikimedia Commons

The Roving Princess

A puzzle by University College London mathematician Matthew Scroggs: A princess lives in a row of 17 rooms. Each day she moves to a new room adjacent to the last one (e.g., if she sleeps in Room 5 on one night, then she’ll sleep in Room 4 or Room 6 the following night). You can open one door each night. If you find her you’ll become her prince. Can you find her in a finite number of moves?

Click for Answer

Sanity Check

https://pixabay.com/en/beach-island-palm-trees-nature-1844962/

From Raymond Smullyan: Every inhabitant of this island either a knight or a knave. Knights always tell the truth, and knaves always lie. Further, every inhabitant is either mad or sane. Sane inhabitants always answer questions correctly, and mad ones always answer incorrectly. You meet an inhabitant of the island and want to know whether he’s sane or mad. How can you determine this with a single yes-or-no question?

Click for Answer

For Pi Day

https://mobile.twitter.com/Cshearer41/status/1054674051388661760

From the prolifically interesting Catriona Shearer: The red line is perpendicular to the bases of the three semicircles. What’s the total area shaded in yellow?

Click for Answer

E Pluribus Unum

Replace each * with a different digit 1-9 to make this equation true:

\displaystyle \frac{*}{**} + \frac{*}{**} + \frac{*}{**} = 1

Click for Answer

The THOG Problem

https://commons.wikimedia.org/wiki/File:THOG.png
Image: Wikimedia Commons

I have picked one color (black or white) and one shape (square or circle). A symbol that possesses exactly one of the properties I have picked is called a THOG. The black circle is a THOG. For each of the other symbols, is it (a) definitely a THOG, (b) undecidable, or (c) definitely not a THOG?

Cognitive psychologist Peter Wason invented this puzzle in 1979 to demonstrate some weaknesses in human thinking. In pilot studies, 0 of 10 student barristers were able to solve it correctly, with one arguing for more than an hour against the correctness of Wason’s solution. Seven of 14 medical students solved it, taking an average of 6.3 minutes. (“This is quite an impressive result.”) One young doctor solved it in his head in about a minute and said, “I would not let any doctor near me who couldn’t solve that problem.” What’s the answer?

Click for Answer

A Pretty Puzzle

https://www.reddit.com/r/mathpuzzles/comments/as1rye/found_this_out_in_the_wild/

I don’t know who came up with this; I found it on r/mathpuzzles. What’s the area of the red region?

Click for Answer

Loose Change

penny puzzle

You’re holding a penny, and you’re standing on an infinite plane. The plane bears a grid of squares, each of which is twice the width of the penny. If you roll the penny out onto the grid, what is the probability that it will come to rest entirely within a square? (Assume the lines are of negligible thickness.)

Click for Answer