# Questions tagged [mathematics]

A puzzle related to mathematical facts and objects, whose solution needs mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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### Chaos and Order: a visual puzzle in stained glass

I created a visual puzzle, which my wife then implemented as part of a stained-glass window. I've no idea if it is (a) obvious, (b) stupid or hopefully (c) extremely clever, and hence would love to ...
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### How can 64 = 65?

Here is a interesting picture with two arrangements of four shapes. How can they make a different area with the same shapes?
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### The Sheikh dies

The Sheikh dies, leaving behind three sons, 17 camels and the following order: His oldest son shall inherit one in two camels. His middle son shall inherit one in three camels. His youngest son shall ...
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### Is this duplo train track under too much tension?

My kids were making this train track of duplo the other day, and this is what they put together. They are still very young, and for them, this is something big. They were really proud that they ...
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### Paying the Troll toll

You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made. Between your house and her house, you have to cross 7 ...
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### 100 Prisoners' Names in Boxes

Names in Boxes The names of 100 prisoners are placed in 100 wooden boxes, one name to a box, and the boxes are lined up on a table in a room. One by one, the prisoners are led into the room; each may ...
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### Prove that π > 3

It seems that once upon a time some politicians tried to pass a law fixing the value of π to be exactly 3. The idea being to "make math simpler so that our children can get better at math". ...
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### Make all the statements true

Can you make all the below statements true with a single click? If yes, explain how. Three + Eleven = Ten Seven + Five = Six Two + Four = Eight NB: 'A Single Click' means, with only a single left ...
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### Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
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### Coin Flipping Game with the Devil

You die, and awake in Hell. Satan awaits you, and has prepared a curious game. He has arranged $n$ quarters in a line, going in the east/west direction. He placed the coins at the ends tails up, and ...
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### Nine gangsters and a gold bar

One night nine gangsters stole a gold bar. When the time came for dividing the bar, they faced a problem: two of the criminals put guns to each other's faces. Now it's up to fate whether one of them ...
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### A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
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### Can you fold a square into a square of one-fifth the area?

I love origami, and it recently gave me an idea for a very hard but beautiful puzzle. I'm really curious whether anyone here can solve it. So here's the puzzle. You are given a large perfectly square ...
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### 10 Prisoners, 10 Keys, and 7 Years

One day, the warden of a prison is, like most wardens in puzzles, feeling a little bit capricious and decides that he wants to get rid of his prisoners, one way or another. He gathers all the ...
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### Making π from 1 2 3 4 5 6 7 8 9 [closed]

There have been two other questions here and here that are similar to this one, but this changes the rules up a little. Your job is to approximate $\pi$ using the sequence of digits (in order): 1 2 3 ...
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### A secret polynomial

Alice has a secret polynomial $P$ with positive integer coefficients. When Bob gives Alice a positive integer $n \neq 2016$, Alice replies with the value of $P(n)$. After doing this several times, Bob ...
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### Are there eighteen or twenty bars in my castle?

Two friends, Mark and Rose, are very famous logicians; they are so clever that they can deduce any logic connection possible in a matter of minutes even from the most vague situation. Unfortunately, ...
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### Can the Policeman catch the Thief?

The town of Squareshire has six streets: four sides of a square and the lines joining the midpoints of opposite sides. $\hskip2in$ A policeman is chasing a thief along these streets. If they are ...
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### Bar-coded Message (Reverse Engineering)

This weekend, while totally minding my own business and in no way being suspicious, I just happened to come across the following interesting document: Left page: download as TIFF (100,203,616 bytes) /...
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### Make 0 0 0 0 = 8

Can you find a way to make: $0\ 0 \ 0 \ 0 = 8$ by adding any operations or symbols? You can use only these symbols: $+,\ -,\ *,\ !,\ /,\ \hat\, ,\ ()$. It is limited to this list, and ...
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### Three mathematicians are forever in Prison

I'm excited to share the following riddle. It was given to me more than two years ago and I finally solved it last summer (after not thinking about it for a long time). In my desperation, I tried to ...
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### Happy Pi-Day! Try to solve this "PiDoku"

To celebrate the Pi-Day (3/14) adequately, a challenging math puzzle must not be missing. Rules: Fill in the numbers 1-9 exactly once in every row, column, and region. On top of that, you need to ...
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### A walk of 3000 meters, but one foot has moved more, how so?

My math teacher has struck again. Here's his newest riddle: Today I went for a normal walk of 3000 meters. One of my feet had to move exactly 3000 meters. However, the second foot moved 3100 meters. ...
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### The Jeweller's Dilemma

You are well known as the best jeweller in Puzzovania; your shop is always well stocked and your pockets are always bulging. One day, the local 'godfather' of Puzzovania's organised crime comes into ...
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### Is it always possible to balance a 4-legged table?

A perfectly symmetrical small 4-legged table is standing in a large room with a continuous but uneven floor. Is it always possible to position the table in such a way that it doesn't wobble, i.e. all ...
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### 2 Monkeys on a computer [closed]

(a) Two monkeys are typing capital letters (A-Z) randomly. The first stops typing when the word COCONUT appears as seven successive letters. The second stops typing when TUNOCOC appears; TUNOCOC is ...
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### XOR - Is it possible to get a, b, c from a⊕b, b⊕c, a⊕c?

Just got a simple question from a friend; still thinking. Let's share it! Is it possible to get a, b, c when you have a⊕b, b⊕c, a⊕c ? where ⊕ is the boolean ...
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### Find a straight tunnel

There is a circular area with radius 1 km. And there is a tunnel, which is just under the surface, but invisible - unless you dig. It is known that the tunnel goes under the area (at least touches it ...
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### The Circular Prison of Unknown Size

You are the president of a secret society of mathematicians with $n$ members, including yourself. No one in the society knows what $n$ is. The dictator of the world, in an effort to erase mathematics ...
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Suppose you have 100 lbs of cucumbers and these cucumbers consist of 99% water. You decide to leave the cucumbers in the sun for a while until they consist of 98% water. You bring the cucumbers back ...
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### Can you explain these equations?

Anthony just got a new drone with an HD camera and microphone, and he is eager to test it out. He connects his computer to its wireless live video stream, opens up his window, and flies it outside. ...
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### A new way to cut a pizza

Can you cut a pizza (circle) into 12 congruent pieces, such that half of them have crust (circle boundary), while the other half do not? The pieces must have the same shape and area, but can be ...
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### The Case of the Miscalculating Calculator

At the Arithmetic Company, to try and cut down labor costs the administration commissioned a calculator to be made. The calculator was produced, and in the quality control division was tested with the ...
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### Does the drunk man fall off the cliff? (a random walk problem)

A drunk man stands with a cliff one step to his left. He takes steps randomly left and right. Each step has probability $p$ of going left and probability $q=1-p$ of going right. Each step is the same ...
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Mathematical Rebus II Mathematical Rebus III $$4\sum_{n=0}^{\infty}\frac{(-1)^n}{2n+1}\\ (-\infty,...,-1,0,1,...,\infty)\times(-\infty,...,-1,0,1,...,\infty)\\ \forall\begin{bmatrix}{-1}&{0}\\ ... • 2,726 52 votes 5 answers 5k views ### Prime Number Snake Place numbers 1 to 100 in the cells of the 10 x 10 board below in such a way that consecutive numbers occupy neighboring cells (either horizontally or vertically). Shaded cells should contain only ... 51 votes 5 answers 7k views ### A man possesses a large quantity of stamps James Joseph Sylvester was one the greatest British mathematicians of the 19th century, who made many fundamental contributions to number theory, combinatorics, and invariant theory. In 1884, he ... • 45.7k 51 votes 6 answers 5k views ### Eight coins for the fair king You are responsible for creating new types of coins for the court. King respects the forgetful: he wants you to create 8 coins of different value, no more. King respects the feeble: he wants that any ... • 6,962 51 votes 2 answers 6k views ### Six pyramids in a cube This question is from the German mathematics competition Känguru der Mathematik. In this competition students have to solve 30 mathematical tasks like this in 90 minutes without calculator. Actually ... • 5,948 50 votes 11 answers 18k views ### Function that is 1 for all positive integers but 0 at 0 A friend of mine had a simple question (at least to state) that I thought I would share: can you, without the use of indicator functions, find a(n) (elementary) function that satisfies \begin{cases} ... • 705 50 votes 7 answers 11k views ### How many tries to roll a 6? Suppose you roll a (fair, 6-sided, perfectly ordinary) die repeatedly until you roll a 6. As is well known, the expected (i.e., long-term average over many trials) number of rolls required is 6. Now ... 50 votes 4 answers 3k views ### A colorful dodecahedron Divide a "base" edge of a regular pentagon into three equal parts. Then draw two lines from the base to the center of the other edges such that the lines do not intersect. This splits the ... • 1,849 50 votes 2 answers 2k views ### lolcatz can haz ur infinit cheeseboard This is a problem on an infinite chessboard with pieces called lolcatz. They can move like queens or knightriders, but have a strange disadvantage... ... you've never heard of knightriders? Well, ... • 5,198 49 votes 11 answers 288k views ### 6, the magic number Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ... • 2,466 49 votes 3 answers 4k views ### The vicious wizard...and you! The vicious wizard Neville has trapped you in the middle of a magical circle of radius 10000, and you have to find a way out. Every time you want to take a step (of length 1) in a certain ... • 12.6k 49 votes 4 answers 16k views ### I don't know the two numbers... but now I do Two perfect logicians, Summer and Proctor, are told that integers 𝑥 and 𝑦 have been chosen such that 1 < 𝑥 < 𝑦 and 𝑥 + 𝑦 < 100. Summer is given the value 𝑥 + 𝑦 and Proctor is given ... • 2,374 48 votes 4 answers 3k views ### Pythagorean Chess: Knishops In chess, Knights moves to squares a distance \sqrt5 away. Bishops move distances \sqrt2, \sqrt8, \sqrt{18}, etc. Both pieces are restricted to non-integer distance moves. Enter the Knishop, ... • 4,400 47 votes 2 answers 5k views ### Ten numbers on a blackboard The numbers 1 through 10 are written on a blackboard. You erase two numbers of your choice, and write their product plus their sum$$a,b \to ab+a+b So, now there are nine numbers on the board. You ...
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The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For ...