Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [puzzle]

For questions about the mathematical principles behind puzzle, games, riddles, or their possible solutions. Questions that are not strictly mathematical in nature should be asked on Puzzling Stack Exchange.

Many puzzles, games, and riddles are based on mathematical concepts. This tag is for questions that ask about the mathematics behind a puzzle, game, or riddle, or about the solutions to mathematical puzzles.

If you already know the answer to the puzzle you are posting, you might consider posting your question on Puzzling Stack Exchange, instead. If you do end up posting your question on Mathematics Stack Exchange (MSE), please read the following meta posts on these kinds of questions before asking your question:

If you do end up posting on MSE, please make it clear in your question that you are "puzzling" the community and that you will be answer the question yourself if no one in the community posts your desired solution.

3301 questions
302
votes
39 answers

One question to know if the number is 1, 2 or 3

I've recently heard a riddle, which looks quite simple, but I can't solve it. A girl thinks of a number which is 1, 2, or 3, and a boy then gets to ask just one question about the number. The girl can only answer "Yes", "No", or "I don't know," and…
Gintas K
  • 765
39
votes
5 answers

How many squares actually ARE in this picture? Is this a trick question with no right answer?

This is one of those popular pictures on sites like Facebook. I always see a huge variation of answers such as $8, 9, 16, 17, 24, 28, 30, 40, 41, 52,$ etc., yet I've never seen a definitive answer on any website. I counted $16$ whole squares ($4$…
user1092719
  • 573
31
votes
1 answer

Mosquito in the Room (Puzzle)

Pondering about a very real mosquito in my room I came up with this puzzle: You are in a room of dimensions $10$ m $\times$ $10$ m $\times$ $3$ m. There is also a (point-shaped) mosquito in the room but you do not know where (the mosquito is…
user88046
31
votes
10 answers

how to find the balls?

You have 15 balls, 2 of them are radioactive. You have to run 7 tests (no more) on the balls which will sort out the 2 radioactive ones guarenteed every time. You can test them in groups, or even one by one. A "test" comprises of taking a subset of…
linus
  • 311
25
votes
8 answers

Google Interview Question about a town where if a couple has a girl born, they can't have more children...

Today I was reading about Google Interview math puzzles and I couldn't solve the following puzzle. Imagine a town where there is a law: If a couple have a girl born, then they can't have more children. If they have a boy born, then they can have…
bodacydo
  • 3,922
23
votes
1 answer

Is every factorial divisible by its sum of digits?

Denote by $\Sigma_d(t)$ the sum of digits in the decimal representation of the number $t$. Prove / disprove: $$\forall n\in \mathbb N:\ \ \Sigma_d (n!) | n!$$
R B
  • 2,426
23
votes
4 answers

"In a circle of 33, the next 10 people on my right are all liars"

In the land of Truthlandia, each person is either a truth teller who always tells the truth, or a liar who always tells lies. All 33 people who gathered for a meal in Truthlandia at a round table, said: "The next 10 people on my right are all…
Jmaxmanblue
  • 479
21
votes
1 answer

Talks using just two words, such that the same thing is never said three times in a row

A bit more than 20 years ago, the following exercise was assigned to a class as the Christmas holiday exercise. I did search for a while whether it was posted here earlier, and could not find it. I guess I might as well ask it as a New Year's Eve…
user20266
21
votes
9 answers

The Three Princesses (distinguishing truth-teller with 1 question)

Is it possible to solve this problem: A prince wish to marry a princess. There are 3 princesses, one is young, one is a little older and one is old. The prince is able to tell the princesses apart. One of the princesses always tells the truth, one…
utdiscant
  • 3,201
17
votes
3 answers

How to check if a 8-puzzle is solvable?

I have a 8-puzzle 1|2|3 -+-+- 4|5|6 -+-+- |8|7 How can be checked if the puzzle is solvable? Wikipedia states that it is solvable, but does not prove it. Can anybody explain the prove?
ceving
  • 271
16
votes
2 answers

Is the game 2048 always solveable?

Games got me on math. I always want to play best. I don't know how to answer my question. My question is : How to show that the game 2048 is (always) solvable>? Is there any method other than brute force? There is a sudko grid and you use…
yiyi
  • 7,352
15
votes
3 answers

What is the mathematical explanation for this trick?

I found the following method to find one's age. It is working exactly for my case. I like to understand and solve this puzzle. If this is wrong forum, my sincere apologies. Please guide me solve this. Take last digit of your mobile number Multiply…
rajakvk
  • 269
15
votes
3 answers

Puzzle: digit $x$ appears $y$ times on this piece of paper....

There are ten questions on a piece of paper. Your task is to fill in each blank with a positive integer less than 10 such that there is no contradiction. You can reuse any digit. The question is as follows: Digit 0 appears __ times on this…
Display Name
  • 2,715
14
votes
4 answers

A logic problem. No need for calculation

Three people were told to go to a cave and each pick up a hat in pitch dark. The three then came out of the cave with the hat on their heads. There were five hats in the cave. Three of them are black, the rest is white. When the first one is asked…
most venerable sir
  • 1,689
13
votes
1 answer

What is special about square numbers here?

I'm not not schooled in math. I'm 50 years old and I only have about a grade 8 level. But I do enjoy math and heard a question in the show "Growing Pains of a Teenage Genius" that interested me. So please forgive me. I do not speak "math." The…
DeeH
  • 141
1
2 3
…
34 35