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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6
votes
7answers
995 views

To equip hand sanitizers

There was an event held by a group. In this COVID-19 era, there were many hardships in equipping quarantine supplies, in addition to carrying out the event. Several bottles of the same hand sanitizer ...
14
votes
3answers
422 views

Two integer sided equilateral triangles with integer distances

In this figure with two non-congruent equilateral triangles and three-fold rotational symmetry the distance between any two of the 6 vertices is an integer. Can you give a solution? I know only one ...
3
votes
2answers
196 views

Determine minimal number of moves to find cells on a square table 10×10 in which a treasure is hidden

In a 10x10 square table, two neigbouring 1x1 cells contain a hidden treasure. John needs to guess these cells. In one move he can choose some cell of the table and can get information whether there is ...
0
votes
1answer
35 views

A rectangle with non-integer side lengths [duplicate]

Is it possible to build a gapless rectangle with non-integer side lengths using rectangles each with two integer side length and two non-integer side length? The rectangles are not required to be the ...
2
votes
2answers
491 views

Lightbulbs in a 3×3 square

Suppose we have a $3\times 3$ arrangement of lightbulbs and we switch them on/off randomly (probability $Β½$). What is the probability the no adjacent bulbs are on? My attempt was: Let $1= $ on and $0 =...
6
votes
2answers
335 views

Twin primes and divisibility

Let $p$ and $q$ be a pair of twin primes. Find the smallest possible value of $a+b$ where $a$ and $b$ are positive integers such that $p\;|\;(a+qb)$ and $q\;|\;(a+pb)$. This puzzle is my own ...
1
vote
2answers
80 views

No four cells forming a rectangle

You are given a 5x5 square grid with 25 cells. Can you paint 12 cells, such that no 4 painted cells form the corners of a rectangle with sides parallel to the edges of the grid? Good luck!
9
votes
3answers
1k views

No three points in a line

You are given a 4x4 square grid. It has 16 cells and 25 grid intersections. Can you place 10 points at grid intersections, such that no three points lie on the same straight line? Lines can be ...
5
votes
2answers
190 views

Running Out of Digits, Level 3

The challenge idea is credited to HelloWorld1337. You initially have x of each digit from 0 to 9. This means you have x * 10 digits in total. This count for each digit is shown in the table below. ...
8
votes
1answer
197 views

Functional equation: composition to get quadratic

Consider the following functional equation: $$f(f(x))=x^2+x-7\quad\quad\forall\; x\in\mathbb{R}.$$ Does there exist a function $f:\mathbb{R}\to\mathbb{R}$ satisfying this, or not?
6
votes
2answers
451 views

Covering a 15x15 grid with rectangles

You are given a 15x15 grid and asked to cover it with rectangles whose dimensions are a power of 2. For example you can use rectangles 8x1 and 4x4, but not 2x3. The rectangles must cover every cell of ...
4
votes
3answers
412 views

Functional inequality?

Find all functions $f:\mathbb{R}\to\mathbb{R}$ s.t. for all $x,y\in\mathbb{R}$, we have $$yf(x)+f(y)\ge f(xy)$$ Problem from the my math olympiad training problem set few weeks before. Functional ...
10
votes
1answer
342 views

A Cryptic Cryptarithm

An entry in Fortnightly Topic Challenge #48: Unusual tag mix Solve these puzzles to reveal why I made them. Matriarch mostly prepared oats for American airline location? (8) AIRLINE + LOCATION = ? 51 ...
5
votes
1answer
286 views

Triangles, rectangles, nonagons

Which is the nonagon with the least area and which fulfills the following conditions. The nonagon has to be made from 7 triangles and 3 rectangles, all having side-lengths that are integer numbers. ...
0
votes
0answers
157 views

The nice and round sequence

I have thought up a sequence, and I name it the nice and round sequence. Its first 10 numbers are 15773, 29694, 165083, 276316, 496325, 498512, 702504, 719466, 808667, 826245 What is its pattern? ...
-4
votes
2answers
117 views

maximum product of n positive integers whose sum is k [closed]

We have to find n numbers such that $$ x_1 + x_2 + \cdots + x_n = k $$ $$ x_1 * x_2 * .....* x_n = maximum $$ What are the values of $x_1, x_2...x_n$ ? Note that $x_1, x_2...x_n$ are all positive ...
4
votes
4answers
581 views

maximum product of n numbers whose sum is k [closed]

We are given two numbers, n and k. We have to find n numbers such that $$ x_1 + x_2 + \cdots + x_n = k $$ $$ x_1 * x_2 * .....* x_n = maximum $$ What are the values of $ x_1, x_2, ...x_n$ if these ...
9
votes
2answers
606 views

A Triangle of Squares

Let $T(n) = 1 + 2 + 3 + \text{...} + n$ be the $n$th triangular number. For which $n>1$, if any, is it possible to split the first $\frac{n(n+1)}{2}$ positive integers into $n$ sets, all of ...
10
votes
1answer
423 views

Grid infection with diagonal adjacencies

A community consists of 81 houses laid out in a 9 x 9 square grid. Every household is friends with their eight orthogonal and diagonal neighbors (except for the houses on the perimeter which have only ...
15
votes
5answers
644 views

Domino tiling on 8x8 checkerboard with four squares removed

I once posted this problem on the (now deleted) Area 51 Math Puzzles proposal. It was well-received there, but obviously I didn't get an answer. I still don't know the answer, and I'm not even sure if ...
2
votes
4answers
200 views

The Greenhouse Problem version 2

This is an extension of Nilster's great puzzle: The Greenhouse Problem The task is the same, but this time sprinklers cover only a 3x3 square around them. For completeness, here is the full set of ...
2
votes
1answer
169 views

How long will it take to hand out the shuffled papers?

A teacher has $n$ students sit in a circle in her classroom. She holds in her hands a perfectly shuffled stack of the students' graded homework, with Juan's on top. She is currently standing in front ...
4
votes
2answers
284 views

Mathematics for the English major

An entry in Fortnightly Topic Challenge #48: Unusual tag mix I was looking at the unusual tag mixes post, and one of the ones listed is combinatorics and english. I thought "who's going to be ...
3
votes
2answers
392 views

3 x 2 sliding puzzle

Would it be possible to solve a sliding puzzle like this (x is the space)?: 1 3 2 4 5 x I haven't been able to solve this and I don't even know if it's ...
5
votes
3answers
221 views

Is this Prime Sequence the longest?

So you are interested in Prime Numbers and puzzles thereof. You saw the following on PSE and gave it a try and got it long after the correct answer was posted by @hexomino. My Eight Cousins But then ...
6
votes
1answer
235 views

Foo Clue and Who?

A simple puzzle I thought of during a work-from-home-session today. Enjoy :)
3
votes
2answers
131 views

What is the house number in nolteight street

Alice moved to nolteight street. Bob meets her after her move, and he knows that the smallest house number in nolteight street is 8, and the highest number is 100. But he does not know Alice's house ...
10
votes
2answers
360 views

Concave quadrilateral with integer sides and integer diagonals

Which is the concave quadrilateral with integer sides and integer diagonals with the smallest possible perimeter? This puzzle is my own creation.
9
votes
4answers
918 views

How to find the 2021st integer co-prime to 15

I recently saw a puzzle where you were to find the 2021st positive integer co-prime to 15 (it was phrased in terms of a game but this is the mathematical core). I wrote code to find the answer but can’...
8
votes
1answer
168 views

My Eight Cousins

My eight cousins are all a different prime number of years old, and their average age is a whole number. Recently they all came to visit me and, as they left one by one, I noticed that at all times ...
1
vote
2answers
211 views

Dividing the first 10 primes into groups whose sum is prime [closed]

Take the first 10 primes. Can you divide them into $g$ disjoint groups, such that the sum of numbers in each group is prime. In particular can you make this work for every value of $g$ in the range $[...
-2
votes
1answer
122 views

Heptagon, nonagon

What is the trick to constructing a heptagon and a nonagon which have all their sides equal? The length of the side has to be a natural number. Your answer should include a drawing of the two polygons....
8
votes
2answers
281 views

Cutting a shape into two equal area shapes

Given the following shape - an hexagon ABCDEF of which a parallelogram CDGH is cut out. With a single cut divide the shape into two equal area shapes by means of an unmarked . You may draw lines and ...
1
vote
3answers
90 views

5x5 grid with no tetrominoes containing repeating colors

Paint the cells of a 5x5 grid with 𝑛 colors, such that every possible tetromino found in the grid uses 4 different colors. What is the smallest value of 𝑛 possible in such a coloring? Here is a ...
3
votes
3answers
356 views

4x4 grid with no trominoes containing repeating colors

Paint the cells of a 4x4 grid with 𝑛 colors, such that every possible tromino found in the grid uses 3 different colors. What is the smallest value of 𝑛 possible in such a coloring?
1
vote
2answers
103 views

A number built with two-digit primes

What is the largest number, which can built as a sequence (from left to right) of different two-digit primes only? For example, 1371731 is valid, 137131 is invalid (containing 13 twice), 139717 is ...
7
votes
1answer
670 views

Finding the median of 5 numbers

There are 5 boxes labeled A, B, C, D and E. Each box contains a distinct number, but you don't know what it is. You can select three boxes and the Oracle will tell you which box contains the median* ...
6
votes
3answers
570 views

Table of mathematical expressions - fill in 1-9

Fill in the numbers 1 through 9 in the 9 empty cells (each number appears exactly once) to make the row and column expressions equal to the number at the end of the row or column. Regular math ...
3
votes
2answers
94 views

A triangle inside a triangle

All sides of a triangle T1 are shorter than the shortest side of a triangle T2. Is it always possible to put triangle T1 completely inside triangle T2?
0
votes
1answer
97 views

Gaby's 21 students sitting around a circle [closed]

Gaby numbers her 21 students with the primes between 11 and 97. She now asks them to sit around a circle making sure that any two of them sitting next to each other have either their tens or units ...
-4
votes
1answer
105 views

How to open the lock from this safe?

The puzzle is as follows: The figure from below shows a lock mechanism used to store sensitive data microfilms from a certain lab. This mechanism is magnetic and consists in numbered buttons which ...
3
votes
2answers
460 views

How to fill 1/3 of the cylinder?

You are given 3 containers - pictured in this order below: a box with side 2, height 1, and a cone with base radius 1 and height 1 in the middle. a box with side 2, height 1, and a half sphere with ...
6
votes
2answers
263 views

Pandigital fraction sum that evaluates to 1

Fill in the nine X spots in the following equation using each of 1, 2, ..., 9 exactly once, so that the equation is satisfied. The XX in the denominator denotes concatenation of two digits. $$ \frac{X}...
-4
votes
2answers
83 views

A challenge to make 1 - 100 [closed]

So this challenge is you have (don't have to) make the numbers 1 - 100 by using the numbers 1, 3, 4, 6 only once. I'm stuck on how to make 54. Can anyone help me? P. S. You can use +, -, Γ·, x, ! And ...
2
votes
1answer
119 views

How many 𝑛-digit integers have the property that the block of its first 𝑘 digits is a prime or divisible by 𝑘 for all 1 ≀ 𝑘 ≀ 𝑛?

Are there infinitely many integers with the property that the block of its first π‘˜ digits (for all π‘˜, 1 ≀ π‘˜ ≀ 𝑛, where 𝑛 is the number of its digits) is either a prime number or is divisible by π‘˜...
7
votes
4answers
596 views

Divided by Pie Squared. Aaahhh

I have a machine that can divide a square pie into 9 equal square pieces using 4 blades: The blades can be moved, but there is only one control - which defines the width of the blades in both ...
2
votes
2answers
310 views

Four touching circles

Three identical circles are placed such that they touch each other. A larger circle is drawn around the smaller circles such that it touches them, as shown in the diagram. Can you find the ratio ...
5
votes
4answers
552 views

8x8 square with no adjacent numbers summing to a prime

Can you fill a 8x8 grid with numbers from 1 to 8 such that: Every number occurs exactly once in each row and in each column (Latin square). No two adjacent (horizontally or vertically) numbers sum to ...
2
votes
1answer
70 views

4x4 square with no increasing triples

Can you fill a 4x4 grid with numbers from 1 to 4 such that: Every number occurs exactly once in each row and in each column (Latin square). No row or column contains 3 adjacent numbers that are all ...
20
votes
2answers
1k views

Not so random walk

I'm out for a very long walk, and I’m bored, so I decide to walk in a mathematical way. The first image shows the first 500 steps, and the second image is my path after 50000 steps. The colors are ...

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