Category Archives: Puzzles and Problems

The King of the Spiders

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Continuing the logic thread, this is a nice logic problem from MathsJam Shout for April 2025.

“The king of the spiders has four servants, and the servants have either 6, 7, or 8 legs.  Servants with 7 legs always lie, and servants with 6 or 8 legs always tell the truth.

The king asks ‘How many legs do you four have in total?’, and the four spider servants (who are standing behind a table, so you can’t see their legs) answer 25, 26, 27, and 28, respectively.

Who is telling the truth?”

Answer.

See The King of the Spiders for a solution.

Logical Card Test

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This is a logical puzzle from Muhammad Zain Sarwar on Puzzle Sphere.

“Real Psychological Puzzle that will Test your Logical Thinking

Only 10% of Participants gave the Right Answer!

Imagine in front of you there are four cards placed on a desk. Each card has a number on one side and a color on the other. The visible faces of the cards show the following:

  • 3
  • 8
  • Red
  • Brown

You are given a rule to verify:

“Every card that shows an even number on one side, then the opposite side must be red.”

Puzzle Statement

Your task is to determine which cards you must flip over to check whether this rule is being followed or not.

This question was part of a real psychological experiment.”

(I emphasized the “must” in the puzzle statement in order to limit the number of cards flipped to the minimum.)

See Logical Card Test for a solution.

A Number Maze

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Here is an entertaining puzzle from Futility Closet.

“By Wikimedia user Efbrazil. Begin at the star. The number at your current position tells you the number of blocks that your next jump must span. All jumps must be orthogonal. So, for example, your first jump must take you to the 1 in the lower left corner or the 2 in the upper right. What sequence of jumps will return you to the star?”

See A Number Maze for solutions

Impossible Homework

This is a somewhat unusual problem from Presh Talwalkar.  It involves proving a student’s homework problem is impossible.

“I came across a homework problem described as “scary” on Reddit AskMath. You need to fill in the number sentences using the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly once.

You should try a few possibilities to see why this is a challenging question. And do not waste too much time because the exercise is literally impossible!  The challenge is, can you prove no solution exists?”

See Impossible Homework for a solution.

Circular Ant Problem

This is a wicked variation of the ant problem on a stick by Peter Winkler.

“Twenty-four ants are randomly placed on a circular track of length 1 meter; each ant faces randomly clockwise or counterclockwise.  At a signal, the ants begin marching at 1 cm/sec; when two ants collide they both reverse directions.  What is the probability that after 100 seconds, every ant finds itself exactly where it began?”

Answer.

See Circular Ant Problem for solutions.

Tricky Triangle

I think this turned out to be an even trickier problem than Alex Bellos thought.

“Tricky triangle  This one was sent in by a reader, aged 85, who first saw it in 1960. He is a roboticist who passed through Harvard, Princeton, Stanford and IBM. He says it is his favourite puzzle. ‘I’ve given this puzzle to perhaps 100 people. Over 80% have no idea how to solve it.’  What is the length of AD, the dashed line?”

Answer.

See Tricky Triangle for solutions.

Cat and Mice

This is a classic puzzle from Boris Kordemsky’s 1972 Moscow Puzzles.

“Purrer has decided to take a nap.  He dreams he is encircled by 13 mice: 12 gray and 1 white.  He hears his owner saying: “Purrer, you are to eat each thirteenth mouse, keeping the same direction.  The last mouse you eat must be the white one.”  Which mouse should he start from [eat first]?”

Answer.

See Cat and Mice for a solution.

The Josephus Problem

This famous Josephus Problem presented on Youtube is somewhat different from the Cat and Mice puzzle, but still has similarities.  An article by Jay Bennett discussing the problem was published in Popular Mechanics in 2016.

 

Penn and Teller – Spelling Cards

It turns out that Penn and Teller have performed another magic trick recently that is based on mathematical principles and so is more or less self-working.  It is a more complicated version of the Cat and Mice puzzle, which I have dubbed the “Spelling Cards” trick. Continue reading →

Fill in the Blanks

This is a fun puzzle from John Bassey at Puzzle Sphere.

“The diagram shows a heptagon with three circles on each side. Some circles already have the numbers 8 to 14 filled in, while the remaining circles need to be filled with the numbers 1 to 7. Each circle must contain one number, and the sum of the numbers in every set of three circles along a line must be the same.  Arrange the numbers!!!”

Answer.

See Fill in the Blanks for a solution.

Chinese Quadrilateral Puzzle

This is another intimidating puzzle from Presh Talwalkar:

“Thanks to Eric from Miami for suggesting this problem and sending a solution!

From a 5th grade Chinese textbook: In the quadrilateral ABCD, angle A = 90°, angle ABD = 40°, angle BDC = 5°, angle C = 45°, and the length of AB is 6. Find the area of the quadrilateral ABCD.”

Answer.

See the Chinese Quadrilateral Puzzle for solutions.

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