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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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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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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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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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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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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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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votes
9
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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 ...
user88
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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
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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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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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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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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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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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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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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 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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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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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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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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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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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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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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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 ...
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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 ...
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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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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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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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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 ...
anon
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6, the magic number
Here's a fun (albeit difficult) one:
Make these equations true using arithmetic operations:
...
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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$$
So, now there are nine numbers on the board. You ...
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Pythagorean Chess: Knishops
In chess, Knights moves to squares a distance $\sqrt5$ away. Bishops move distances $\sqrt2$, $\sqrt8$, $\sqrt{18}$, etc. Both pieces are restricted to non-integer distance moves.
Enter the Knishop, ...
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x⌊x⌊x⌊x⌋⌋⌋ = 2020
Solve for $x$:
$$
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 ...
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What percentage is grey?
The evenly spaced lines are drawn parallel to the base of triangle. What percentage of the triangle is grey?
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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 ...
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