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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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180 votes
1 answer
11k 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 ...
MattClarke's user avatar
  • 2,033
143 votes
8 answers
46k 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?
ʇolɐǝz ǝɥʇ qoq's user avatar
133 votes
8 answers
24k 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 ...
Alexander's user avatar
  • 2,443
129 votes
5 answers
142k views

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 ...
Lezzup's user avatar
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127 votes
12 answers
30k 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 ...
Shevliaskovic's user avatar
122 votes
7 answers
30k 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 ...
Jaydles's user avatar
  • 2,007
118 votes
3 answers
12k 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". ...
Florian F's user avatar
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117 votes
8 answers
8k 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 ...
AeJey's user avatar
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99 votes
7 answers
25k 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 ...
WendiKidd's user avatar
  • 2,453
93 votes
9 answers
14k 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 ...
Mike Earnest's user avatar
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88 votes
18 answers
17k 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 ...
Glinka's user avatar
  • 1,317
85 votes
16 answers
209k 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 ...
user avatar
83 votes
5 answers
8k 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 ...
Mitsuko's user avatar
  • 2,035
81 votes
10 answers
19k 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 ...
Milo Brandt's user avatar
  • 7,881
79 votes
15 answers
16k 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 ...
Glen O's user avatar
  • 5,023
78 votes
3 answers
6k 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 ...
rnaylor's user avatar
  • 2,611
75 votes
21 answers
31k 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, ...
Marco Bonelli's user avatar
74 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 ...
Ankoganit's user avatar
  • 19k
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) /...
2012rcampion's user avatar
  • 18.9k
69 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 ...
SteamCode's user avatar
  • 3,181
67 votes
7 answers
12k 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 ...
LFH's user avatar
  • 797
67 votes
2 answers
7k 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 ...
NAMELESS's user avatar
  • 1,370
66 votes
8 answers
18k 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. ...
Paul Karam's user avatar
  • 2,221
66 votes
5 answers
12k 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 ...
Rand al'Thor's user avatar
65 votes
12 answers
17k 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 ...
Rand al'Thor's user avatar
65 votes
15 answers
11k 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 ...
anmol porwal's user avatar
64 votes
12 answers
26k 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 ...
Jet's user avatar
  • 775
58 votes
8 answers
6k 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 ...
klm123's user avatar
  • 16.2k
57 votes
7 answers
10k 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 ...
Mike Earnest's user avatar
  • 32.4k
55 votes
8 answers
18k 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 ...
NL628's user avatar
  • 7,490
55 votes
6 answers
4k 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. ...
pacoverflow's user avatar
  • 15.2k
54 votes
3 answers
16k 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 ...
Dmitry Kamenetsky's user avatar
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 ...
KSab's user avatar
  • 1,142
53 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}\\ ...
Masclins's user avatar
  • 2,726
52 votes
7 answers
21k 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 ...
DanielSank's user avatar
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 ...
Bernardo Recamán Santos's user avatar
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 ...
Gamow's user avatar
  • 45.6k
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 ...
Thomas Blue's user avatar
  • 6,952
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 ...
A. P.'s user avatar
  • 5,948
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 ...
49 votes
11 answers
288k views

6, the magic number

Here's a fun (albeit difficult) one: Make these equations true using arithmetic operations: ...
ThreeFx's user avatar
  • 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 ...
leoll2's user avatar
  • 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 ...
durron597's user avatar
  • 2,374
48 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} ...
Therkel's user avatar
  • 685
48 votes
4 answers
2k 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 ...
Herbert Kociemba's user avatar
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, ...
Johannes's user avatar
  • 4,392
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 ...
xnor's user avatar
  • 27k
46 votes
10 answers
189k 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 ...
user avatar
46 votes
12 answers
5k views

What percentage is grey?

The evenly spaced lines are drawn parallel to the base of triangle. What percentage of the triangle is grey?
Simd's user avatar
  • 7,845
46 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 ...
Roman Odaisky's user avatar

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