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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1answer
21 views

Factorizing complex numbers

Let's have the following number $(3i-\frac{5}{3})^3$. What is the trick to factorizing this number in more than one way?
1
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0answers
12 views

Fill in 6x6 magic multiplicative magic square

Let's say you fill in a 6 by 6 square with the numbers 1, 2, ..., 36. Is there a way to fill it so that the product of the first row is equal to the product of the first column, the product of the ...
-4
votes
1answer
98 views

A Clear, Simple, Geometry Problem [closed]

Draw a shape consisting of all the points equidistant from a specific point. Furthermore, draw a segment passing through a side of the shape exactly twice, and draw another segment so that it also ...
4
votes
1answer
371 views

Fill in a 4x4 multiplicative magic square

Suppose we have 4 by 4 grid with numbers 1, 2, .., 16. Can we fill the grid so that the product of the first row is equal to the product of the first column, the product of the second row is equal to ...
0
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1answer
161 views

Least cuts can be made in a metal grid structure to get 44 rods

The puzzle is as follows: Suppose that you have a metal structure made by brass wire. Assuming that you must get 44 rods of the same size each. What is the least cuts to be made using an electric ...
1
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1answer
107 views

Minimum cuts to make a rectangle into a square, allowing bending

The puzzle is as follows: Mike has a thin sheet of cardboard which is 96 centimeters large by 24 centimeters wide and a guillotine whose maximum cut length is 80 cm. Assuming this guillotine can cut ...
2
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1answer
177 views

Fill in a 5x5 multiplicative magic square

Let's say you fill in a 5 by 5 square with the numbers 1, 2, ..., 25. Is there a way to fill it so that the product of the first row is equal to the product of the first column, the product of the ...
0
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1answer
93 views

Vowels, consonants and Mathematical Shapes

Your aim is first to select at least three different mathematical shapes. For instance, you could select "a losange", "a disk" and "two lines". You must then ensure that ...
3
votes
1answer
156 views

Universal bisectors

A bisector is something that cuts some other thing into two equal pieces. More concretely, assume we are given a reasonably well-behaved (for example, compact) 3D object and we are looking for planes ...
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0answers
81 views

Bisecting a 3D object into two equal volume objects - 2

Given the following 3D object and means of an unmarked ruler to draw lines on its surface define a straight cut that will split it into two objects with the same volume. Hint: It seems to have at ...
3
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2answers
176 views

Primes and squares in a grid

i) Place thirteen different three-digit prime numbers in the empty cells of this grid. ii) Now place thirteen different three-digit square numbers in the empty cells of this grid. How many solutions ...
-5
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1answer
87 views

Relations between numbers taken three at a time [closed]

Let's have the following numbers. $(5i+\frac{1}{2})$, $(2i+3)$, $(\frac{-101}{8})$, $(7i+4)$, $(5i+1)$, $\frac{(40i-97)}{8}$. How are these numbers related when taken three at a time? Operations ...
4
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1answer
1k views

Find three ways of forming the number 100 using 3,3,5,7

As it says in the title. Rules: anything not explicitly allowed is forbidden. use 3, 3, 5, 7 and multiplication, division, sum, difference, unary minus, and exponentiation in any order. Parentheses ...
10
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1answer
164 views

Three white queens, two white knights, and one rook on a chess board

On an 8 x 8 chessboard, place three white queens, two white knights, and one white rook so that every cell of the board is under attack by at least one piece not standing on it. Source: https://www....
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0answers
88 views

Hard IQ Test Puzzle [closed]

Can someone please help me to find the answer to the puzzle?
0
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1answer
78 views

Number of turns for two wheels to bring edge-points together

The puzzle is as follows: We present you below this riddle. A certain mechanism opens a gate of a maximum security lab. It just happens that a glass lets you see the mechanism and you know the ...
2
votes
0answers
61 views

Fair and square island hopping [duplicate]

If amateur fiction is not your thing skip to the bottom. As IP (Implausible Physics) expert for DREAM, the Department for Reckless Engineering and Advanced Megalomania you have been tasked by sheikh ...
8
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3answers
577 views

Calculation - the hard way

This is a puzzle I love to play with my math students and I hope you will enjoy it too: You are given the numbers 1, 2, 3, 4, and 5 exactly once. Your target is a number, e.g. 36. Can you create a ...
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0answers
63 views

Finding the hypotenuse of a right angle triangle when one side has been given [closed]

If one side of a right angle triangle has length equal to $a^{n-1}$, where $n\ge2$ and $a$ is any odd number greater than 1, how do we find the length of the hypotenuse? The lengths of the sides of ...
5
votes
1answer
218 views

How to get the least possible sum in a closed loop set of squares?

The puzzle is as follows: The figure from below represents a set of 12 squares joined forming a closed loop. By using only the numbers from 1 to 12 fill in the blanks. The condition is that, without ...
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2answers
146 views

How many lines are needed to connect all smiling toasters in a 4x4 grid?

The puzzle is as follows: How many straight lines do you need to draw the least possible to join all the smiling toasters if you should not raise the pen or go over any line already drawn? Remember ...
4
votes
1answer
321 views

Two knight tours on a 4x4 grid

Two knights are placed on opposite corners of a 4x4 grid. Can you move* each knight 7 times, such that each cell of the grid is visited exactly once by exactly one of the knights? *Note that a knight ...
1
vote
2answers
224 views

Minimize the longest King chain on a 6x6 ternary grid

This puzzle is an extension of this one: Minimize the longest King chain on a 5x5 binary board Given a grid filled with numbers, we define a King chain to be a path on the grid such that: The path ...
0
votes
1answer
120 views

Minimize the longest King chain on a 7x7 binary grid

This puzzle is an extension of this one: Minimize the longest King chain on a 5x5 binary board Given a grid filled with numbers, we define a King chain to be a path on the grid such that: The path ...
5
votes
0answers
188 views

Choosing squares on a square board [closed]

I have an $8 \times 8$ board. On the board, I want to choose 2 unit squares in each column and row such that none of the chosen squares are touching. This means they cannot share a side or a corner. ...
13
votes
1answer
2k views

A Math Riddle: But the math does not add up

Grandpa had a lot of different books of stamps on his desk. He was counting them. I was curious. “What are all those stamps Grandpa?” “I just got back from the Post Office son and bought a bunch of ...
4
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2answers
233 views

All possible locations of a robot going from $(x,y)$ to $(x+y, y)$ or $(x,x+y)$ [closed]

Suppose I had a little robot on the coordinate grid that moves according to the following rule. If it's at the point $(x,y)$, it can move to either $(x+y,y)$ or $(x,x+y)$. If the robot starts at the ...
-1
votes
1answer
130 views

Solving the equation $A^4=B^4+C^4$ [closed]

Let's have the following numbers: $2\sqrt7$, $\sqrt{\frac{7\sqrt{674}-168}{2}}$, $3\sqrt7$, $-\sqrt{\frac{7\sqrt{674}-168}{2}}$, $2\sqrt7$ Can you put these numbers into three different groups A,B,C ...
3
votes
2answers
88 views

Dividing the first 10 numbers into two groups with similar product

Can you paint all numbers from 2 to 10 with red and blue colour, such that the product of all red numbers is as close as possible to the product of all blue numbers?
-1
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0answers
46 views

How to find the number of knight-routes moving upwards to the top of the board [duplicate]

In chess, a knight moves in L-shaped jumps consisting of two squares along a row or column plus one square at a right angle. If it can only move up the board, how many routes can it take to reach any ...
-2
votes
2answers
105 views

How many have to enter the building so their birthday matches?

The riddle is as follows: Looking at his watch a doorman from an hotel in New York notices that 280 people are inside. Suddenly he begins to ponder the following. How many people should have to come ...
3
votes
1answer
137 views

Seven letters riddle

Hoping it is a never-seen riddle, here is the problem. We have seven letters A,B,C,D,E,F,G. Each letter is associated with a unique number between 1 and 10. We know the following: D is 3 units ...
13
votes
7answers
824 views

Minimize the longest King chain on a 5x5 binary board

Given a grid filled with numbers, let's define a King chain to be a path on the grid such that the path can be traversed with chess King's moves (moving to one of 8 adjacent cells at a time), the ...
6
votes
7answers
988 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
408 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
0answers
77 views

Placing trominoes on an 8X8 grid [duplicate]

Let's have two 8x8 grids which each have 21 trominoes of three different colors, 7 trominoes of each color. Can you put these trominoes on the grid without two of the same color touching anywhere. In ...
3
votes
2answers
192 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
486 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 $½$). What is the probability the no adjacent bulbs are on? My attempt was: Let $1= $ on and $0 =...
6
votes
2answers
333 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
79 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
189 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
195 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
449 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
407 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
331 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
283 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
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0answers
155 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
113 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 ...

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