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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3 views

Wait, it is worth it?

You went to a Casino, and saw a quite interesting stall. The cardboard besides the stall says: You first pay \$$5$ You have to toss the fair coin. If it lands heads, you can ...
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2answers
77 views

Tangential circles

The following figure has two axes of symmetry which define its width and length. The length (horizontal distance) is twice the width (vertical distance). The largest circle has a radius of 2005 and ...
6
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2answers
228 views

Probability of picking the red marble twice

Start with a bag containing one red marble and one white marble. Reach into the bag and pull out a marble at random. Put it back and do it again. If, on both times, you grabbed the red marble, stop. ...
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4answers
297 views

Floor functional equation

Find all functions $f:\mathbb{R}\to\mathbb{R}$ satisfying the following functional equation: $$f(\lfloor x\rfloor y)=f(x)\lfloor f(y)\rfloor\quad\quad\text{for all }x,y\in\mathbb{R},$$ where $\lfloor\...
7
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1answer
295 views

A functional equation again!

Determine all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$(x-2)f(y)+f\big(y+2f(x)\big)=f\big(x+yf(x)\big)$$ for all $x,y\in\mathbb{R}$. Source: Math Excalibur Volume 22, Number 1 ...
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1answer
122 views

Mathematical golfing

You have probably heard of code golfing? There the task is to find the shortest computer program that produces the required output. Here we want to perform math golfing - find the shortest formula ...
7
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1answer
254 views

120 degrees and circles

The bigger circle has a radius of $1$, and it is tangent to the two straight lines that forms an angle of $120$ degrees. The smaller circle is tangent to the two straight lines and the big circle. ...
12
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3answers
898 views

Random walking on a board

There’s a pawn starting in the center of this game board. At each move, it can advance randomly towards any of the adjacent squares sharing a common side with equal chance. What’s the probability of ...
9
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0answers
141 views

A fairy tale in a golden toy

Once upon a time, long long ago, in the days when good stories were far more beautiful and far harder to come by, a king was asked by his spoilt but beloved princess daughter to give her a fairy tale. ...
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8answers
6k views

9-5=5? Matchstick problem

Move one matchstick to make an equality. Question made by me (Is this too easy?)
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2answers
86 views

Complete this cross sequence

What is the next element of this sequence and why? Possible choices:
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1answer
175 views

Three squares in a triangle

In a triangle, three identical squares of side lengths 2.8 share a common vertex and are each touching two sides of the triangle. If one of the angles in the triangle is 75 degrees and is opposed to a ...
7
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2answers
637 views

A Covid-19 puzzle: Alcohol for your School!

You are the principal of a primary school in HK. Schools are resuming soon, and you have to ensure that your school have enough alcohol. Each of the 30 classrooms should have a bottle containing 500mL ...
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3answers
590 views

Knight and Knaves Castle

I was pretty bored in the lockdown so I thought up a mathematics puzzle, which I haven's solved yet, so the community can solve together. Let $n>1$ be a positive integer. There is a square ...
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1answer
114 views

demystify and paint me!

To demystify me, look and say. Then paint me not with colors but with array. ...
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0answers
80 views

Missing number in a set of four segment circles

This is a puzzle posted on a social networking site that I have been trying hard since yesterday to solve: My approach has been to find out a mathematical function with the numbers in the yellow, ...
11
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5answers
372 views

Move just 2 matchsticks to make three equally sized triangles

There are 9 equally sized matchsticks, move 2 to make 3 equal triangles
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8answers
2k views

Create an equation using the following numbers and mathematical symbols: 4,2,1,2,4,+, =

Create an equation using only the following numbers and mathematical symbols: $$4,2,1,2,4,+,=$$
11
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8answers
2k views

n(n+1) as a multiple of 100

Here's a puzzle I came up with while walking today: For how many natural numbers $n$ is the number $n(n+1)$ a multiple of $100$? This is true for infinitely many $n$, so "how many" means something ...
9
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1answer
281 views

Functional Equation: Squeeze it

Determine whether there exists a function $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f\big(x^3+x\big)\le x\le\big(f(x)\big)^3+f(x)$$ for all $x\in\mathbb{R}$. Source: Math Excalibur Volume 22 No....
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3answers
3k views

How many ways can you find the word DIAMOND in this diamond?

In how many different ways may the word DIAMOND be read in the arrangement shown? You may start wherever you like at a D and go up or down, backwards or forwards, in and out, in any direction you like ...
9
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1answer
499 views

Functional equation involving 2020th powers

Find all functions $f:\mathbb{N}\to\mathbb{N}$ which satisfy $$ (n-1)^{2020}<\prod_{k=1}^{2020}f^{(k)}(n)<n^{2020}+n^{2019}\quad\quad\text{for all }n\in\mathbb{N}, $$ where $\mathbb{N}$ is the ...
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2answers
114 views

Find a factor #1

The series of Find a factor puzzle is started by Culver Kwan, and asks the solver to identify a factor of a certain large number within a certain range using some mathematical identities. This should ...
6
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2answers
178 views

The pond of symmetry

There is a $4$m by $4$m square pond. You have $3$ straight planks of wood, each exactly $2$m in length. You need to place the planks so that they go from one corner of the pond to the diagonally ...
7
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1answer
108 views

Number to Alphanumeric Mapping

A certain website uses the following mapping to encode their integer ID to an alphanumeric string. Can you figure out what the mapping is? ...
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4answers
3k views

A COVID-19 puzzle: How large a class do you need to fit 30 pupils?

Some countries are proposing to reopen high schools soon. To ensure safety, they want to make sure that all pupils in a class are at least 2 m apart. To help them find the smallest room that can ...
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0answers
51 views

A Dices Probability Riddle [duplicate]

Bob (A), Steven (B) and Joe (C) were playing with dices, each one of them made his own dice and wrote a number between 1-6 on each side of his dice. After playing for a while they've noticed that : (...
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5answers
867 views

Wizard creating a jewelry

I have a puzzle game which I am not sure how to prove that I have the right answer. The Puzzle is the following: We have a wizard which makes very special jewelry (a straight line with beads). ...
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2answers
619 views

A risky investment

I invested $1000 into shares. On the first day the share price went up by 10%. On the second day it went down by 10%. This process continued - the share price would go up by 10% on odd days and down ...
4
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1answer
103 views

Numbers Relation Puzzle

I've written a numbers relation puzzle, I'd like to share it with you and see what you fellas think. ------ Try to find the relation between the numbers------ Good to know: there are 2 parameters ...
7
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1answer
288 views

Frog in the Well [duplicate]

A frog is trapped in a well, just 1 meter below the lip. On sunny days, the well is dry, and the frog is able to climb up 1 meter. On rainy days, the well is wet and the frog slides down 1 meter. If ...
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3answers
145 views

Find the relation between these numbers

I've just joined and wanted to contribute a bit myself so here are 3 puzzles my friend made to test me, first two I've solved but third one stomped me, see if you can solve it yourself! First one - ...
3
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1answer
186 views

A graph logical task - Ramsey theory

I have the following puzzle and I want to check if the answers that I gave are correct. You can check also my reasoning behind the answers. The puzzle is: In a perfect world two people are either ...
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1answer
131 views

Find relation between the following numbers with use Elementary arithmetic

Find relation between the following numbers: we can use only Elementary arithmetic (addition, subtraction, multiplication, and division) . I find this puzzle in my old book .I think we have ...
8
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2answers
264 views

Another follow the path of relation through the grid

Inspired by Galen's series of puzzles...there is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-...
10
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2answers
300 views

Alice, Bob and Charlie know the sum, product and the difference between two numbers

This was sent to me by a friend so I can't source it but here's the full text: Three Mathematics students, Alice, Bob and Charlie have to find the values of $x$ and $y$, with $x, y \in \mathbb Z, ...
4
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1answer
150 views

Three tables, One logic and Nine numbers to guess

Here is a table divided in three parts, the first two (the green and the yellow ones) are completely clear, while the last one (which is red) has 9 numbers to guess (α1, β1, γ1, δ1, α2, β2, γ2, δ2 and,...
4
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1answer
173 views

Cutting a Rectangular Board

There is an $m \times n$ rectangular board drawn on a graph paper. You need to cut it into $mn$ $1 \times 1$ squares by straight cuts along the grid lines. You are allowed to stack several pieces ...
5
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2answers
221 views

Achieve the best outcome by a tactical statement

This puzzle is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which bargaining power is gained, paradoxically, by burning bridges and removing options for oneself. Here it ...
2
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0answers
92 views

Probabilities for “What number is that? — asks grandpa”

Inspired from Multilanguage generalization of "What number is that? Asks Grandpa" and What number is that ? Asks Grandpa In this puzzle we will use the English alphabet of 26 letters. We ...
9
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0answers
224 views

Dead By Daylight

This puzzle is a reference to a game, Dead By Daylight. Though you don't need a knowledge about the game. Consequently, there is no "video-games" tag. Story The Entity wants to have the killers' ...
13
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6answers
1k views

Create integers using 1, 2, 3, 4, 5, 6, 7 and +, -

There are numbers $1, 2,3,4,5,6,7$ and signs '$+$' and '$-$'. Using only these numbers and signs, you can compose expressions and calculate the sum (difference). Concatenation operation is not valid. ...
11
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1answer
282 views

Gaby´s Puzzle (Primes Around a Circle)

To keep them busy during lockdown, Gaby asked her children to find a way to place the first sixteen primes (2 to 53) around a circle so that either the sum or difference (or both) of any two of them ...
6
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2answers
435 views

Logical task for math

I have one Math puzzle to which I think I found the solution but wanted to check your opinion on it. The puzzle is the following: George has 1 banknote of 100 (the currency does not matter. Lets name ...
4
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1answer
70 views

Follow the path of relation through the grid #9

There is a relation between rectilinear-adjacent squares such that there is a unique rectilinear path from the top-left corner of the grid down to the bottom-right corner of the grid. Each square can ...
24
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0answers
508 views

Ridiculous problem from an old maths textbook

There's a puzzling little problem I found in one of my old maths textbooks (Basics of Madthematics). In the middle of a whole bunch of normal problems on calculus and algebra and whatever, suddenly ...
10
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1answer
501 views

His reputation went up!

Today, a new user John created an account on PSE, and he got an association bonus. He answered a question. Few days later, after logging in, his reputation went up! (He did not do any other things ...
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0answers
514 views

What is the Color Code™?

Inspired from Can you name the country code? and What is a Number™? series $ \begin{gather} % custom template - reuse if you may \def\S#1#2{\Space{#1}{21px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}}...
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1answer
50 views

What's the graph relation? #4

What's the relation that joins the nodes? Previous What's the graph relation? #1 What's the graph relation? #2 What's the graph relation? #3
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1answer
162 views

What's the graph relation? #3

What's the relation that joins the nodes? Previous What's the graph relation? #1 What's the graph relation? #2

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