Check out this new puzzle book for upper-level high school students & adults:

Thomas Povey is a Professor of Engineering Science at the University of Oxford, where he researches jet-engine and rocket technology. In his new book Professor Povey’s Perplexing Problems, he shares his favorite idiosyncratic stumpers from pre-university maths and physics.

These problems “should test your ability to grapple with the unfamiliar,” Povey writes. “You will learn to tease new problems apart, and apply things you already know in ways you had never considered. You have all the tools you need, but you should see what amazing things you can do with them.”

Can You Solve This?

Alex Bellos shared one of Professor Povey’s puzzles in The Guardian. Can you figure it out?

The book starts off with geometry, but most of the chapters focus on various topics from physics. Some of the puzzles are accessible through applied common sense, but for many of them, it helps to have taken an algebra-based (high school level) physics course.

Kitten is just finishing up her physics textbook, and she still has one more year of homeschooling. I’m hoping to work several of these puzzles into our schedule this year. It should be great fun!

Spoiler

If like me you’re a bit rusty on your physics, don’t worry. Each answer is thoroughly explained—in fact, it takes a bit of discipline to close the book and try your hand at each problem before reading on. I wish they’d put the solutions in the back rather than in the main text, to make it easier to browse the problems without reading spoilers.

Speaking of which, here’s the answer to the video puzzle above…

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The August “Let’s Play Math” newsletter went out last week to everyone who signed up for Tabletop Academy Press math updates. This month’s issue focuses on logic puzzles for all ages, including a newly-discovered deleted scene from Harry Potter and the Sorcerer’s Stone. What fun!

If you missed this month’s edition, no worries—here are some great puzzles from the Let’s Play Math blog archive:

There will be more playful math snacks coming in September. Click the link below to sign up now, and we’ll send you our free math and writing booklets, too!

One of the most persistent math myths in popular culture is the idea that mathematics is primarily about getting right answers.

The truth is, the answer doesn’t matter that much in math. What really matters is how you explain that answer. An answer is “right” if the explanation makes sense.

And if you don’t give an explanation, then you really aren’t doing mathematics at all.

Try This Number Puzzle

Here is a short sequence of numbers. Can you figure out the rule and fill in the next three blanks?

2, 3, 5, 7, ___, ___, ___, …

Remember, what’s important is not which numbers you pick, but rather how you explain your answer.

Possibility #1

Perhaps the sequence is the prime numbers?

2, 3, 5, 7, 11, 13, 17, …

The prime numbers make a wonderful sequence, though it isn’t the one I was thinking of.

Math Concepts: division as equal sharing, naming fractions, adding fractions, infinitesimals, iteration, limits Prerequisite: able to identify fractions as part of a whole

This is how I tell the story:

We have a cake to share, just the two of us. It’s not TOO big a cake, ‘cuz we don’t want to get sick. A 8 × 8 or 16 × 16 square on the graph paper should be just right. Can you cut the cake so we each get a fair share? Color in your part.

How big is your piece compared to the whole, original cake?

But you know, I’m on a diet, and I just don’t think I can eat my whole piece. Half the cake is too much for me. Is it okay if I share my piece with you? How can we divide it evenly, so we each get a fair share? How big is your piece?

How much of the whole, original cake do you have now? How can you tell?

I keep thinking of my diet, and I really don’t want all my piece of cake. It looks good, but it’s still just a bit too big for me. Will you take half of it? How big is that piece?

Now how much of the whole, original cake do you have? How could we figure it out?
[Teaching tip: Don’t make kids do the calculation on paper. In the early stages, they can visualize and count up the fourths or maybe the eighths. As the pieces get smaller, the easiest way to find the sum is what Cohen does in the video below—identify how much of the cake is left out.]

Even for being on a diet, I still don’t feel very hungry…

In the land of Fantasia, where people communicate by crystal ball, Wizard Mathys has been placed in charge of keeping the crystal connections clean and clear. He decides to figure out how many different ways people might talk to each other, assuming there’s no such thing as a crystal conference call.

Mathys sketches a diagram of four Fantasian friends and their crystal balls. At the top, you can see all the possible connections, but no one is talking to anyone else because it’s naptime. Fantasians take their siesta very seriously. That’s one possible state of the 4-crystal system.

On the second line of the diagram, Joe (in the middle) wakes up from siesta and calls each of his friends in turn. Then the friends take turns calling each other, bringing the total number of possible connection-states up to seven.

Finally, Wizard Mathys imagines what would happen if one friend calls Joe at the same time as the other two are talking to each other. That’s the last line of the diagram: three more possible states. Therefore, the total number of conceivable communication configurations for a 4-crystal system is 10.

For some reason Mathys can’t figure out, mathematicians call the numbers that describe the connection pattern states in his crystal ball communication system Telephone numbers.

Can you help Wizard Mathys figure out the Telephone numbers for different numbers of people?
T(0) = ?
T(1) = ?
T(2) = ?
T(3) = ?
T(4) = 10 connection patterns (as above)
T(5) = ?
T(6) = ?
and so on.

Hint: Don’t forget to count the state of the system when no one is on the phone crystal ball.

Feature photo at top of post by Christian Schnettelker (web designer) and wizard photo by Sean McGrath via Flickr. (CC BY 2.0) This puzzle was originally featured in the Math Teachers At Play (MTaP) math education blog carnival: MTaP #76.

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Six years ago, my homeschool co-op classes had fun creating this April calendar to hand out at our end-of-semester party. Looking at my regular calendar today, I noticed that April this year starts on Wednesday, just like it did back then. I wonder when’s the next time that will happen?

A math calendar is not as easy to read as a traditional calendar — it is more like a puzzle. The expression in each square simplifies to that day’s date, so your family can treat each day like a mini-review quiz: “Do you remember how to calculate this?”

The calendar my students made is appropriate for middle school and beyond, but you can make a math calendar with puzzles for any age or skill level. Better yet, encourage the kids to make puzzles of their own.