# 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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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?
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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....
88 views

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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
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### 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?
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...