How many triangles do you see?

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A post shared by Popular Mechanics Magazine (@popularmechanics) on Jan 29, 2020 at 12:14pm PST

Sure, you can count them. I did, and, er, I missed a few. Or you can take one of the approaches suggested by the mathematics professors that Andrew Daniels interviewed in Popular Mechanics:

“I would approach this just like one approaches any mathematical problem: reduce it and find structure,” says Sylvester Eriksson-Bique, Ph.D., a postdoctoral fellow with the University of California Los Angeles’s math department.

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Can you figure out what number comes next?

Take a look at the sequence. What number comes next? The answer is a no brainer – once you know the answer, that is.

Neil Sloane, founder of the Online Encyclopedia of Integer Sequences, starts explaining the answer at :22, so pause before then if you need more time to figure it out.

Extra footage of this video can be found here. Read the rest

Puzzle - how to ensure you get the quarter, not the penny

From our friends at Futility Closet:

Here are a penny and a quarter. Make a statement. If your statement is true, then I’ll give you one of these coins (not saying which). But if your statement is false, then I won’t give you either coin.

Raymond Smullyan says, “There is a statement you can make such that I would have no choice but to give you the quarter (assuming I keep my word).” What statement will accomplish that?

Answer is here. Read the rest

Can you solve the seven planets riddle?

Created by esteemed riddler Edwin F. Meyer, co-author of The Gedanken Institute Book of Puzzles.


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Excellent $5 puzzle book: The Moscow Puzzles: 359 Mathematical Recreations

I bought the Dover edition The Moscow Puzzles in 2014, and it's still one of my all-time favorite puzzle books. Here are a few samples:

Book description:

This is, quite simply, the best and most popular puzzle book ever published in the Soviet Union. Since its first appearance in 1956 there have been eight editions as well as translations from the original Russian into Ukrainian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold.

Part of the reason for the book's success is its marvelously varied assortment of brainteasers ranging from simple "catch" riddles to difficult problems (none, however, requiring advanced mathematics). Many of the puzzles will be new to Western readers, while some familiar problems have been clothed in new forms. Often the puzzles are presented in the form of charming stories that provide non-Russian readers with valuable insights into contemporary Russian life and customs. In addition, Martin Gardner, former editor of the Mathematical Games Department, Scientific American, has clarified and simplified the book to make it as easy as possible for an English-reading public to understand and enjoy. He has been careful, moreover, to retain nearly all the freshness, warmth, and humor of the original.

Lavishly illustrated with over 400 clear diagrams and amusing sketches, this inexpensive edition of the first English translation will offer weeks or even months of stimulating entertainment. It belongs in the library of every puzzlist or lover of recreational mathematics.

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Can we wrap a 1x1x1 cube with the blue 3x3 piece of paper, cutting along some edges without disconnecting it?

Here's a good puzzle that Clifford Pickover found at CTK Insights:

Is it possible to wrap the cube with a 3×3 piece of paper below it? Handling of the paper is subject to two conditions:

1. The paper may be only cut or folded along the crease lines.

2. The cutting should not cause pieces to separate.

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Can you solve the virus riddle?

"Your research team has found a prehistoric virus preserved in the permafrost and isolated it for study. After a late night working, you’re just closing up the lab when a sudden earthquake hits and breaks all the sample vials. Will you be able to destroy the virus before the vents open and unleash a deadly airborne plague?"

A fun Ted-Ed puzzle by Lisa Winer.

[via] Read the rest

A hat puzzle

A good puzzle from our friends at Futility Closet:

Three logicians walk into a bar. Each is wearing a hat that’s either red or blue. Each logician knows that the hats were drawn from a set of three red and two blue hats; she doesn’t know the color of her own hat but can see those of her companions.

The waiter asks, “Do you know the color of your own hat?”

The first logician answers, “I do not know.”

The second logician answers, “I do not know.”

The third logician answers, “Yes.”

What is the color of the third logician’s hat?

Puzzle by MIT mathematician Tanya Khovanova. Click here for answer. Read the rest

Brain teaser: draw a cross inside the grid

On the latest episode of Scam School, Brian Brushwood presented three old brain teasers. Here's my favorite.

Make a five-by-five grid of dots. Then draw a cross by connecting the dots in such a way that five dots are enclosed by the cross and eight dots are outside the cross. The example on the right satisfies the first part (five dots inside the cross) but it fails the second requirement (it has four dots outside, but needs eight.)

You can learn the solution by watching the video. Read the rest

Puzzle: The Candy Thief

A puzzle from our friends at Futility Closet:

Five children — Ivan, Sylvia, Ernie, Dennis, and Linda — entered a candy store, and one of them stole a box of candy from the shelf. Afterward each child made three statements:


1. I didn’t take the box of candy. 2. I have never stolen anything. 3. Dennis did it.


4. I didn’t take the box of candy. 5. I’m rich and I can buy my own candy. 6. Linda knows who the crook is.


7. I didn’t take the box of candy. 8. I didn’t know Linda until this year. 9. Dennis did it.


10. I didn’t take the box of candy. 11. Linda did it. 12. Ivan is lying when he says I stole the candy.


13. I didn’t take the box of candy. 14. Sylvia is guilty. 15. Ernie can vouch for me, because he has known me since I was a baby eight years ago.

If each child made two true and one false statement, who stole the candy?

A problem by Wayne M. Delia and Bernadette D. Barnes:

Click here for answer. Read the rest

The best place to sit in a "suicide circle" if you really don't want to die

Math problems are more interesting when they are posed as horror stories.

The Josephus Problem gets its name from Titus Flavius Josephus, a first-century Jewish scholar.

The story goes that he was with 40 other soldiers when they were surrounded by conquering Romans - imagine that scene in Games of Thrones, where Ramsay Bolton's men trap Jon Snow's army in a tight circle and start moving in.

Rather than give themselves up, the soldiers decided to commit suicide en mass, but by killing each other rather than themselves, to avoid any last-minute changes of heart. Sitting in a circle, the first soldier would kill the man to the left of him, the next living soldier would kill the man to his left, and so on around the circle.

When the circle of slaughter got back to the start, the process would repeat with the smaller group of people. Finally, the last man alive would fall on his sword.

Josephus' problem was that he was much keener on living than dying - but he didn't want to let his fellow soldiers in on that secret. So, where should he position himself in the circle to be the last man standing?

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The best book of physics brain teasers

I bought Thinking Physics, by Lewis C. Epstein in 1984. It's one of my favorite books of brain teasers. They are designed to help you gain a qualitative, intuitive sense of physics. The author stresses that after you read each of the many charmingly illustrated problems in the book, you should put the book away and take your time running a simulation of the problem in your head. This is great advice. Read the rest

The Missing Dollar puzzle from Martin Gardner's Aha! Gotcha book series

Martin Gardner wrote Aha! Gotcha: Paradoxes to Puzzle and Delight and Aha! Insight in the early 1980s and I love them both. Both books have excellent brain teasers with charming illustrations. They are both out of print, which is criminal, but Amazon has used copies for $(removed) (plus $(removed) s&h).

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Build this brain-teasing golf ball in a block of wood

Gareth Branwyn is blogging for Make, and I've been enjoying his posts. Take a look at this golf ball inside a cage that's hogged out of a single piece of wood.

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Saturday morning mind-benders: "Newcomb's Problem" and "Parfit's Hitchhiker" dilemma

In this video Julie Galef, host of the Rationally Speaking podcast (about philosophy, rationality, science) presents one of my favorite paradoxes - Newcomb's Problem (and the related and "Parfit's Hitchhiker" dilemma).

Before Carla and I started the bOING bOING zine, I published another zine in the mid-1980s called Toilet Devil (Koko the talking ape calls people and her pet kitties "dirty toilet devils" when she is mad at them). In the first issue I drew a comic about "Newcomb's Problem." I might scan it one day and post it.

In 2006, I posted about Newcomb's Problem:

Franz Kiekeben does a nice job of describing Newcomb's Paradox, which I've enjoyed contemplating, on and off, for many years.

A highly superior being from another part of the galaxy presents you with two boxes, one open and one closed. In the open box there is a thousand-dollar bill. In the closed box there is either one million dollars or there is nothing. You are to choose between taking both boxes or taking the closed box only. But there's a catch.

The being claims that he is able to predict what any human being will decide to do. If he predicted you would take only the closed box, then he placed a million dollars in it. But if he predicted you would take both boxes, he left the closed box empty. Furthermore, he has run this experiment with 999 people before, and has been right every time.

What do you do?

On the one hand, the evidence is fairly obvious that if you choose to take only the closed box you will get one million dollars, whereas if you take both boxes you get only a measly thousand.

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Pill-popping panic - a good brain teaser

A good puzzle from Futility Closet. Read the rest