# 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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### Do puzzles like "write 120 using four 8" have a specific name?

Here on puzzling SE there is the category "calculation puzzle", but it's very broad. I'd like to know if somebody gave a specific name for such puzzles.
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1 vote
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### How many ways are there to mark a way to walk around every edge of the triforce?

A triforce for the purposes of this question is a plane figure with an equilateral triangle at its center, with one additional vertex connected to each pair of original vertices (forming an additional ...
• 179
1 vote
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### The Police Took a Wonderful Taxi to Oz

Clues: [contextual images] T [scissors] [hand shape] ? [cylindrical contoured container] $\sqrt{(m_{_0}c²) ² + (pc) ²}$ Instructions: Name That Duo _ _ _ _ _ _ D _ _ _ _ _
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### Can you stop copy Alice?

At time 0, Alice and you both move freely at speed 1 on the plane. As each hour passes, all copies of Alice will subdivide into 2, each moving at half the speed of the parent. So if left alone, at ...
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### 2023 From Single Digits

Using only the digits, 1, 2, 3, 4, 5, 6, 7, 8, and 9, in that order, how can you make the number 2023 using the +, -, ✕ and ÷ operations? (You can use as many parentheses as you want)
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### Kangaroo Coordinates

A kangaroo is sitting at the coordinate (1, 1). If the kangaroo is at some coordinate (a, b), it can always jump to (a + b, b) or to (a, a + b). Which positive integer coordinates can the kangaroo not ...
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### I Hate Traffic And So Do You

I need to travel through the city from my house to school, but the traffic is horrible right now. I can only move along the city's grid with the following conditions: • blocks with traffic (marked in ...
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### The minimalist game master [closed]

A game master tells his party of players that he has converted to the school of minimalism, and is going to do away with all of his dice in the campaigns they play from now on. In the place of dice, a ...
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### The Power of Math

If $(M+A+T+H)^4=MATH,$ then what are M, A, T, and H? See if you can also find it for $(P+O+W+E+R)^5=POWER$ (I don't think that it has a solution) and $(T+H+E)^3=THE$
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A four-letter name is encoded A=0 to Z=25. Find a name that satisfies: The sum of the integers answers all, their product is like a boob, and their range is X. Order the integers by increasing ...
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### Triangles, Triangles, and More Triangles

Which has more area, Shape A, which is one big triangle, or Shape B, where each 2 triangles have half the side length of the previous two triangles? (Shape B has infinitely many triangles.) Or do they ...
• 574
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### The Era Of The Ear

Given this information, \begin{matrix} & E & R & A \\ + & E & A & R \\ \hline & A & R & E \\ \end{matrix} What is the sum of $A$, $R$, and $E$ and if you can ...
• 574
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### Cutting a square into integer triangles

You are given a square piece of paper with size 10x10 units. What is the most number of triangles that can be cut from this square, such that: Each triangle has integer sides. Each triangle is ...
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### A prisoner and two dice

A prisoner is offered the following deal. They will be given a pair of standard 6-sided dice to roll. If they can roll a total of 42 or more without rolling a double then they will be set free. ...
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### A multiplicative magic square

How can you transform a given magic square into a square where all the lines are invariant under multiplication?
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### Super Star Numbers

A Super Star Number is a positive integer N, such that the 21 vertices of the super star below can be labelled with different positive integers so that the product of the three numbers in any of its ...
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### 1, 2, 3, 10, ... Another find-the-next-number-in-the-sequence puzzle

Can you spot the pattern and continue the following sequence? 1, 2, 3, 10, 12, 16, 25, 37, 55, 81, 100, ... Hints:
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### Optimal Strategy: Catch Up

There are 5 Quisenaire blocks. The first has length 1, the second has length 2, and so on. Each player will be building their own line of blocks, which is initially empty. A move consists of a player ...
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### What is the next number in the sequence below [closed]

6.000,7.000,.857,8.168,.105,77.790 Which of the following responses completes the series .001 740.857 9.524 .013
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### Shortest time to cook burgers

Attribution: I remember seeing this type of question some time ago but don't remember from where. So I have redesigned the question. Hope that is OK. You have 5 burger patties to grill. Each side ...
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### A Magic Super Star

Place 21 different positive integers on the vertices of this star so that the products of the three numbers in any of the 14 straight lines are all equal. How small can the largest of the numbers be?
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### Fill in the blanks with 1-9: ((.-.)^.)*..+.-.-.-.= 100

This is a math puzzle asked by a teacher of mine that I can't figure out. The puzzle is to fill in all blanks with digits 1-9, using each only once, to equal 100. The equation is as follows: (dots are ...
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### The Music Grunniens V2 [duplicate]

Clues: [music notes] Instructions: Name That Actor _ _ _ _ _ _ C _ _ _ _
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### Rotating teams through stations without repeating a topic?

I am putting together a gallery walk activity and want to rotate 6 teams through 4 unique “topics.” This activity will take place in a rectangular room. There will be 6 “stations” set up. Each station ...
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### Painting a Checkerboard

I love checkers - but I've played it so much that the color of my board is faded and dull. Today, I resolved to paint it. Unfortunately, I slipped and fell :( Now there's paint all over my ...
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1 vote
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### What is the value of x? 16-48-98, 32-->x

What's the value of x? (Original picture) 4 | 8--8--1 16-48-98 | | 32--->x I have four possible answer choices: 130, 132, 160, and 260. I'm not sure which ...
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### Drowning Squirrel

On a super foggy day, a squirrel falls from a tree into a swimming pool. Due to fog, it cannot see any bank of the pool, unless it touches the bank. It is aware that the swimming pool is in the shape ...
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### n*n*n Rubik's cube algorithm

Is there a universally working (I mean, regardless of n) algorithm for Rubik's cube n×n×n ? It is acceptable to divide ...
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### The Halftime Hustle

In a soccer stadium restroom there are 100 stalls (cubicles), arranged in a straight line. Stalls are numbered 1, 2, 3,..., 100, with 1 being closest to the main exit of the restroom. Unfortunately, ...
• 1,063
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### Catch the mouse (Easy)

A mouse is at the center of a square. There are 4 cats each on the mid-points of different sides of the square. Mouse is looking to escape to any corner of the square. Mouse and cats have the same ...
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### Explain this incorrect proof that 3=0

Consider the quadratic equation $x^2+x+1=0$. $x=0$ is not a solution to this equation, so it is safe to divide both sides by $x$. $x+1+\frac{1}{x}=0$ Rearrange: $x+1=-\frac{1}{x}$ And substitute into ...
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### Do non-trivial Skolem squares exist?

Define a Skolem sequence to be a permutation of the sequence of 2n numbers 0, 0, 1, 1, 2, 2, ..., n-1, n-1 in which there are no numbers between the two 0s (the 0s are in adjacent positions), there is ...
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### 2x8 Langford Rectangle

I was inspired by this great puzzle. Can you place each number from 1 to 8 twice into a 2x8 grid, such that each pair of numbers $k$ are separated by Manhattan distance $k$?
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### Do Langford squares exist?

A Langford sequence is a permutation of the sequence of 2n numbers 1, 1, 2, 2, ..., n, n in which there is one number between the two 1s, there are two numbers between the two 2s, and more generally ...
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### Creating a clever hemisphere

Given five points on a sphere, can you always draw an equator such that four or more points lie on one hemisphere? How? Points on the equator count as being on either side.
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### Surprise pi! Explain this phenomenon

Take any scientific calculator and follow these steps: Ensure the calculator is in degrees mode. Enter some number of 5's (more than 4 is ideal). Take the reciprocal of step 2. Take the sine of step ...
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### The "Slightly Spooky Sequence" Game

Two players, Alice and Beatrice, having previously agreed on a positive integer N (say 30) as a limit, take turns to write a sequence of positive integers. In the first turn Alice writes 1. Thereafter,...
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### Lengths of sides of a right-angle triangle [closed]

Let's have a right angle triangle. The sides have lengths equal to rational numbers. The area of the triangle is equal to 39, the length of the hypotenuse is 31.3 and the difference of the other two ...
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### 499 and the Gamma Function

Folks elsewhere in this very same site have been working hard to express positive integers in the binary system using merely four ones and four zeros. They have been allowed to use the four basic ...
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### Save now! All the digits at half the price

... or double the price depending on where you're coming from Consider the set $PD10$ of pan-digital ten-digit numbers, i.e. positive whole numbers whose decimal representation has each of the digits ...
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### Unique number from digits 0123456789 with simple property

It would be fun to have a puzzle "Find the only 10-digit number having each digit once AND property xyz", but offhand I don't know any "simple" xyz. "Is a square" gives ...
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### Flipped Einsteins in the Einstein Tiling

The single-tile aperiodic tiling by Goodman-Strauss, Kaplan, Myers and Smith has been all the rage recently: In this tiling a minority of tiles, coloured purple above, are flipped with respect to the ...
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1 vote
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### Cubes touching one cube [duplicate]

There is one blue cube and many white ones - all of equal size. Try to arrange the white cubes around the blue one so that they touch it. Overlapping is not allowed. Valid touching is considered ...
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### The possibilities keep reducing

You find yourself participating in a thrilling puzzle tournament, prepared for any challenge that comes your way. In front of you, there is a safe. It looks like a large black cube, except for the ...
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### Fair d5 with as few faces as possible

Challenge: design a polyhedral die that will always give one of five outcomes, each with equal probability. While achieving that, minimize the total number of faces of the die. Think of the die as ...
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### Pingala the Pirate

Pingala the Pirate was well known for many things, most notably the urban legend that he had hidden an enormous haul of riches, but also his poor memory, and his clumsiness. He lost a toe on each foot ...
• 357
1 vote
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### Scheme to select a multiple choice answer on a whiteboard secretly? [closed]

Trying to set up a cute demonstration of cryptography, here's what I'm envisioning so far: I have a whiteboard, some number of students, and an equal number of different colored markers. On the ...
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1 vote
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### Average length of chords with a fixed end [closed]

The problem is pretty simple to state. Draw a circumference of radius r, and fix a point on the perimeter. The question is: What is the average length of all the chords defined by that fixed point and ...