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Can you solve the frog riddle? - Derek Abbott

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You're stranded in a rainforest, and you've eaten a poisonous mushroom. To save your life, you need an antidote excreted by a certain species of frog. Unfortunately, only the female frog produces the antidote. The male and female look identical, but the male frog has a distinctive croak.

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The counterfeit coin riddle is derived from the mathematics field of deduction, where conclusions are systematically drawn from the results of prior observations. This version of the classic riddle involves 12 coins, but popular variations can consist of 12 marbles or balls. Part of the appeal of this riddle is in the ease with which we can decrease or increase its complexity. A simple swapping of a few key words drastically alters the problem's difficulty.

To make the problem simpler, for example, we can reduce the total number of coins to 9. To further simplify, we can reveal whether the counterfeit is lighter or heavier at the onset, as is shown here. For a harder version of the problem, start with 39 coins and four weighs.

In all cases, the counterfeit coin riddle offers a fun introduction into the world of deductive reasoning.

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Can you solve the counterfeit coin riddle? - Jennifer Lu

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You're the realm's greatest mathematician, but ever since you criticized the Emperor's tax laws, you've been locked in the dungeon. Luckily for you, one of the Emperor's governors has been convicted of paying his taxes with a counterfeit coin, which has made its way into the treasury.

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Find the original paper by George Boolos here. The riddle belongs to a category of puzzles known as Knights and Knaves, many of which can be found in Raymond Smullyan's classic What is the Name of This Book? For a more in-depth look at these riddles, you can read this overview of the assumptions and possible paradoxes in different versions of the puzzle, or learn more about the law of excluded middle.

Don't forget that TED-Ed has more riddles! For more fun, start with these three:
Can you solve the river crossing riddle? - Lisa Winer
Can you solve the counterfeit coin riddle? - Jennifer Lu
Can you solve the frog riddle? - Derek Abbott

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Can you solve the three gods riddle? - Alex Gendler

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You and your team have crash-landed on an ancient planet. Can you appease the three alien overlords who rule it and get your team safely home? Created by logician Raymond Smullyan, and popularized by his colleague George Boolos, this riddle has been called the hardest logic puzzle ever.

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Can you solve the virus riddle? - Lisa Winer

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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?

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Much of this educator's work concerns a mixture of logic with educated guesses. This educator teaches a class called Heuristic Problem Solving in which students face puzzles every week and write computer programs to solve them. Some of those students have turned those puzzles into two or more people computer games. A few of those games even include an Artificially Intelligent opponent.

Please visit the doctor ecco site to create an account and try the games. The Gravitational Voronoi, No Tipping, and Pandemic games might be a good place to start. Give them a try and see how you do.

Like paper and pencil challenges? This logic book might just be what you are looking for: The Puzzling Adventures of Dr. Ecco. For another book that is much like the previous one, take a look for any logic book by Raymond Smullyan. Try some logic puzzles and see how things go.

Love this riddle? Try another by the same educator: Can you solve the temple riddle? - Dennis E. Shasha

Love the challenge of puzzles and riddles? TED-Ed has more for you - take a look at the following:

Can you solve the locker riddle? - Lisa Winer

The famously difficult green-eyed logic puzzle - Alex Gendler

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Can you solve the control room riddle? - Dennis Shasha

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As your country's top spy, you must infiltrate the headquarters of the evil syndicate, find the secret control panel, and deactivate their death ray. But your reconnaissance team is spotty, and you have only limited information about the control panel's whereabouts. Can you solve the control room riddle and deactivate their weapon in time?

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This passcode riddle is an excellent way to introduce factors and multiples and shows the most effective way to understand organized factorization. A good way to understand this problem is by first understanding how a number can be written as all possible products of t natural numbers. Here is a more detailed explanation of how that can be done. Once we have understood this process of writing a number as all possible products of 2 natural numbers, we can move on to understanding how a number can be written as all possible products of 3 natural numbers. For instance, to find the products of 36, a good way to start off would be to write it as 1*1*36. Next, we can break 36 down further and write it using all possible products of 2 numbers. We should get 1*2*18; 1*3*12; 1*4*9; and 1*6*6. We continue this process to find all possible products of 3 natural numbers.

If you enjoyed this problem, here's another version of a problem with the number 72: "UNSOLVABLE" Logic Puzzle: What Are Their Ages?

You may also visit the educator's website here to understand factors and multiples in detail. Finally, if you wish to understand more math concepts (who wouldn't?), visit this link.

Love riddles? TED-Ed has plenty of them that will challenge you:

The famously difficult green-eyed logic puzzle - Alex Gendler
Can you solve the prisoner hat riddle? - Alex Gendler
Can you solve the control room riddle? - Dennis Shasha
Can you solve "Einstein's Riddle"? - Dan Van der Vieren Can you solve the temple riddle? - Dennis Shasha Can you solve the frog riddle? - Derek Abbott
Can you solve the locker riddle? - Lisa Winer

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Can you solve the passcode riddle? - Ganesh Pai

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In a dystopian world, your resistance group is humanity's last hope. Unfortunately, you've all been captured by the tyrannical rulers and brought to the ancient coliseum for their deadly entertainment. Will you be able to solve the passcode riddle and get everyone out safely? Ganesh Pai shows how.

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This puzzle is an excellent example of creative thinking in math. The origin of this puzzle is the 100 prisoners problem, first published in 2003 by Danish computer scientist Peter Bro Miltersen. The educator for this lesson first came across the puzzle at the Gathering for Gardner conference. What caught their attention was the fact that, counterintuitively, it really does matter how you solve the problem. The idea of labeling the boxes on the outside to create loops reduces the problem to a graph theory problem. If you are not well-versed in combinatorics, it might be quite difficult to count the actual number of loops which lead to failure, that is, those loops that are larger than half the number of band players (or prisoners). In the solution presented in the lesson, we use complete graphs to help count the loops. Counting loops is isomorphic to finding the number of Hamiltonian paths on complete graphs, which for small numbers is quite easy and illustrates a way to reach the solution. Here is another comprehensive explanation of the puzzle.

Puzzles like this belong to a branch of math called recreational math. They are appealing to many people, even those who do not have a mathematical education. They invite people to learn or discover for themselves mathematical concepts 'through the back door'. Recreational math and its use as a stimulant for creative thinking is one of the areas of expertise at the Davidson Institute of Science Education, the educational arm of the Weizmann Institute of Science in Israel. Its use in elementary and junior high school education is applied through the international math and science by mail online programs. They are currently expanding their activities to open courses in recreational math, the first of which, Math Puzzles, is currently available on the Future Learn platform.

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Can you solve the prisoner boxes riddle? - Yossi Elran

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Your favorite band is great at playing music...but not so great at being organized. They keep misplacing their instruments on tour, and it's driving their manager mad. Can you solve the brain-numbing riddle their manager assigns them and make sure the band stays on their label? Yossi Elran shows how.

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Let's Begin...

You and nine other individuals have been captured by super-intelligent alien overlords. The aliens think humans look quite tasty, but their civilization forbids eating highly logical and cooperative beings. Unfortunately, they're not sure whether you qualify, so they decide to give you all a test. Can you solve this hat riddle? Alex Gendler shows how.

Create and share a new lesson based on this one.

About TED-Ed Animations

TED-Ed Animations feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TED-Ed Animation? Nominate yourself here "

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Can you solve the prisoner hat riddle? - Alex Gendler

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You and nine other individuals have been captured by super-intelligent alien overlords. The aliens think humans look quite tasty, but their civilization forbids eating highly logical and cooperative beings. Unfortunately, they're not sure whether you qualify, so they decide to give you all a test. Can you solve this hat riddle?

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The locker problem is often used as an introduction to factors, multiples, square numbers, prime numbers, and sequences. It shows that some problems can be solved using a smaller, simpler problem rather than brute force (also known as the method of exhaustion). Here is a more detailed video solution to the locker problem, and here is a related problem that uses Othello pieces instead of lockers.

If you enjoyed the locker problem, you might enjoy studying figurate numbers. Another fun problem to investigate is the handshake problem. An interesting extension is to write square numbers as the sum of odds. Visit the educator's blog that links these units together, and another that is from the viewpoint of students who learned about it.

Love riddles? TED-Ed has plenty of them that will challenge you:

The famously difficult green-eyed logic puzzle - Alex Gendler

Can you solve the prisoner hat riddle? - Alex Gendler

Can you solve "Einstein's Riddle"? - Dan Van der Vieren

Can you solve the temple riddle? - Dennis E. Shasha

Can you solve the frog riddle? - Derek Abbott

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Can you solve the locker riddle? - Lisa Winer

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Your rich, eccentric uncle just passed away, and you and your 99 nasty relatives have been invited to the reading of his will. He wanted to leave all of his money to you, but he knew that if he did, your relatives would pester you forever.

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Can you solve the river crossing riddle? - Lisa Winer

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As a wildfire rages through the grasslands, three lions and three wildebeest flee for their lives. To escape the inferno, they must cross over to the left bank of a crocodile-infested river. Can you help them figure out how to get across on the one raft available without losing any lives?

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Can you solve the airplane riddle? - Judd A. Schorr

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Professor Fukanō, the famous scientist, has embarked on a new challenge - piloting around the world in a plane of his own design. There's just one problem: there's not enough fuel to complete the journey. Luckily, there are two other planes to help.