# 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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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
138 views

### Black War Heroes or Whites Save the Queens?

After Black Cavalry successfully captured White princesses, White empire learns their Black opponent is hungry for more and wants White Twin Queens dead! White will never let such a disaster happen ...
375 views

### Primes in a Line

Place the first 20 primes (2 to 71) in a line so that the sum or difference (or both) of any two primes that find themselves next to each other is always a perfect square. For which other values of N ...
84 views

### Ideal number of Fruit Baskets

I'm not sure if this is more of a Math or a Puzzling question, but I'll give it a shot here due to it's game related aspects and rules. I've been playing some Runescape lately and while training the "...
107 views

### What is a Special Prime Number™?

This is inspired by the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles, now with numbers. If a number conforms to a special rule, I call it a Special ...
175 views

### Black Cavalry Fork Attack

On this chess optimization puzzle, there are only black knights and white queens. Your aim is that no black knight is threatened and to maximize the total number of queens the knights could capture. ...
455 views

### What is a Chemical Number™?

This is inspired by the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles, now with numbers. If a number conforms to a special rule, I call it a Chemical ...
88 views

### Follow the path of relation through the grid #8

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 ...
111 views

### How can I cut a cube so that all its vertices except for two mutually opposite vertices are equally distanced from the plane of the cut?

A friend of mine has been struggling with a solid geometry problem and, knowing my imagination skills developed by playing gomokunarabe and renju, has asked me to help her, but the problem has proved ...
394 views

### Matchsticks $9+9=8$ [closed]

You are given the matchsticks wrong equation $9+9=8$ and you can move, at most 3 matches. Your aim is to find all correct equations. Selected answer will be one that discovers most correct equations ...
626 views

### Smallest integer whose first n multiples contain the digit 1

For some time now I have been investigating the function $M(n)$, the least integer such that the first $n$ multiples of $M(n)$ contain the digit $1$. Thus $M(3) = 51$, because $51$ is the smallest ...
138 views

### Follow the path of relation through the grid #7

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 ...
173 views

### Q-Puzzle on $\mathbb F_7$

My high school math student had to solve this puzzle for his homework. I made it harder by not telling you what is the definition of $\mathbb{F}_7$. Neither why letter Q is used and which of his ...
82 views

### Follow the path of relation through the grid #6

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 ...
196 views

### How many ways to draw the figure without lifting pencil? [duplicate]

The rules are very simple ... Star at A, end at A. From one point you can to go to the other point by only one line (no turning at cross roads). No going over any line more than once. find the ...
164 views

### Follow the path of relation through the grid #5

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 ...
202 views

### Find a sufficient passcode

"As per corporate policy we need to change the passcode for the building's entrance every six months," said Lionel. "Your job is to pick the new passcode. It must have at least four numbers in it." ...
96 views

### Follow the path of relation through the grid #4

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 ...
301 views

### FORTY9 Cryptarithm

This puzzle is due to the amazing Martin Gardner and I found it here. Can you find which digit each letter represents to make the following sum work? Each letter is a single unique digit between 0 ...
149 views

### Follow the path of relation through the grid #3

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 ...
172 views

### Follow the path of relation through the grid #2

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 ...
249 views

### Follow the path of relation through the grid #1

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 ...
383 views

### Make -132,680 from these operations

Make the result $-132,680$ using these operations and numbers: Numbers (cannot be used more than once, but not all need to be used): $2,4,6,8,9,10,11,12,23,27$ Operations (all operations have to ...
97 views

### Mathematics Puzzle - Number Circle

The numbers 1, 6, 8, 13, 15, and 20 can be placed in the circle below, each exactly once, so that the sum of each pair of numbers adjacent in the circle is a multiple of seven. In fact, there is more ...
176 views

### The sadistic chieftain and the lethal truel game

In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind. "I'll ...
126 views

### When is a robotic arm able to reach any point (closer than the length of the outstretched arm)?

In a plane, there is a robotic arm consisting of $n \ge 2$ segments of length 1, like this: The first segment is fastened to a single point ("origin"), but it can rotate freely around that point. All ...
256 views

### Add a divisor! A game

Let $k$ be a positive integer. Amy and Ben are playing a game, with the number $1$ written on the whiteboard initially. Amy and Ben do the following in order, starting with Amy: Suppose the ...
199 views

### Interplanetary blips and bleeps

Things were quite different in 3000 AD. We'd discovered other planets with sentient life for instance. Five to be precise. Adam, Bill, Carl, Dave, and Eric we called them, and we used the lately ...
613 views

### Perfect Golomb Circles

A Golomb ruler of order $n$ is a straight line with $n$ marks (at integer locations) such that no two pairs of marks are the same distance apart. We can extend the concept to circles. Place $n$ marks ...
227 views

### Ways to destroy a Square Matrix

Sherlock is solving a case where he came across a puzzle. Suppose you are given a square matrix of size $N$, and a gun with Power $F$. Every cell in the matrix is filled with some number, $x$ (...
293 views

101 views

### A man was born in the 18th Century. In certain year of his life, the square of his age was equal to the year. What year was he born? [closed]

He was born in the 18th century, the square of his age was equal to the year he was born.
605 views

### Prime to number conversion

This puzzle relates to Prime to Prime: Get all first 25 Prime Numbers using up to 4 Primes and its sequel Prime to Prime Sequel Using any three of the first 4 prime numbers (2,3,5 and 7) and the ...
1k views

### Confusion on a math puzzle

One of my colleagues asked me below puzzle, Three friends went to a picnic. 1st and 2nd friends collected woods for cooking where 3rd friend did not participated because he was sick. 1st friend ...
535 views

### Find the code from the image

Find the numerical code from the images. You don't get any hints.
105 views

### Can we use only arithmetic operator to make this true [closed]

Can we use only arithmetic operators (no digits) to make this true? 11 11 11 = 6
159 views

### A generalization of the lights-out problem

Look here for the original problem. Let the set $J$ be the set of pairs of positive integers $(m,n)$ with $m\ge n$. Suppose $(m,n)\in J$. Then there are $m$ lights, which they are initially off. ...
295 views

### As you can perfectly see, I'm a strange-looking tree. How old am I?

As you can perfectly see, I'm a strange-looking tree. I grow over generations, never suffering degradations. There's no trick, do not fret, what you see is what you get. I can go on and on, time ...
178 views

### Puzzle - Turn all the lights on

A machine has 2020 lights and 1 button. Each button press changes the state of exactly 3 of the lights. That means if the light is currently on, it turns off, and if the light is currently off, it ...
427 views

### Which gun is Alice's best choice?

Alice, Bob and Charles are involved in a deadly three way duel game. Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
320 views

### Just some simple calculation to return this pattern

Here is a table, inside there are simple operations to perform, but there are also particular numbers that don't have the same logic. So how difficult will it be to find the last number and the ...
378 views

### Consecutive numbers which use all digits a different number of times

Are there arbitrarily long sets of consecutive numbers such that when writing the set down, every single digit (0 to 9) is used a different number of times?
One day, you are caught by a evil wizard. He presents you with a prism, and says, "You can ask me to turn this prism to any $n$-angled right prism. Then you shall fill in $1$ to $3n$ with no ...