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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174 votes
1 answer
10k views

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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139 votes
8 answers
42k views

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?
130 votes
8 answers
23k views

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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124 votes
13 answers
23k views

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 ...
121 votes
7 answers
28k views

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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111 votes
8 answers
7k views

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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110 votes
3 answers
10k views

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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93 votes
7 answers
23k views

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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87 votes
9 answers
13k views

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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86 votes
18 answers
16k views

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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82 votes
15 answers
98k views

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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79 votes
15 answers
15k views

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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79 votes
5 answers
7k views

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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76 votes
10 answers
18k views

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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75 votes
3 answers
5k views

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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73 votes
20 answers
29k views

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, ...
71 votes
5 answers
8k views

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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70 votes
6 answers
5k views

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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68 votes
24 answers
23k views

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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66 votes
2 answers
6k views

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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65 votes
5 answers
11k views

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 ...
64 votes
8 answers
17k views

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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64 votes
7 answers
11k views

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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63 votes
12 answers
24k views

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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62 votes
12 answers
15k views

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 ...
62 votes
15 answers
10k views

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 ...
57 votes
8 answers
5k views

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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54 votes
8 answers
17k views

The Cucumber Paradox

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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54 votes
6 answers
3k views

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. ...
54 votes
1 answer
5k views

Mathematical Rebus

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}\\ ...
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54 votes
3 answers
4k views

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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52 votes
7 answers
8k views

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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51 votes
3 answers
15k views

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 ...
50 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 ...
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50 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 ...
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50 votes
7 answers
19k views

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 ...
49 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 ...
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49 votes
5 answers
4k 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 ...
48 votes
7 answers
10k 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 ...
48 votes
11 answers
287k views

6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
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47 votes
10 answers
185k views

1 2 3 4 5 6 7 8 9 = 100

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 ...
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47 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 ...
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47 votes
4 answers
15k 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 ...
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46 votes
11 answers
16k 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} ...
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45 votes
4 answers
7k views

x⌊x⌊x⌊x⌋⌋⌋ = 2020

Solve for $x$: $$ x \left\lfloor x \left\lfloor x \left\lfloor x \right\rfloor \right\rfloor \right\rfloor = 2020. $$ The floor function $\left\lfloor t \right\rfloor$ has the usual “greatest integer ...
45 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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45 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, ...
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44 votes
17 answers
9k views

A blanket for my baby snake

Mama snake wants to knit a blanket for little baby snake. She is not a dissipater and wants to make the blanket of a minimal size (area). But her baby snake is quite a lively baby and it always ...
44 votes
8 answers
9k views

Haters gonna hate

In a classroom, there are $20$ students and every student mutually hates exactly $3$ other students in the class. (If X hates Y, Y hates X as well.) The principal summons some of the students from ...
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44 votes
5 answers
3k views

What fraction of the larger semicircle is filled?

What fraction of the larger semicircle is filled? The two smaller semicircles are of equal size. This is a puzzle originally set by Catriona Agg, who is a puzzle setting genius.
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