# Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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### Is it possible to put the numbers into circles?

This topic is motivated by the trolley813's answer on my question. Question. Is it possible to put the numbers $1,2,3,...,23$ in circles so that the sum of the four numbers on $9$ sides of $3$ ...
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### Put the numbers $1, 2, …,16$ in circles

Put the numbers $1, 2, 3, ..., 16$ in circles so that the sum of the four numbers on each side of the triangle should be equal.
850 views

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### A Grid With the Products of Its Rows and Columns are the Same Set of Numbers

Lets say there is a $3 \times3$ grid that is filled with the numbers $1,2,3,...9$ Can the numbers be arranged so that the products of the columns are the same set of numbers as the product of the rows ...
107 views

### Sum of All the Others

There are ten different 10-digit decimal fractions, one of them being equal to the sum of the other nine. If each number has 10 unique digits, not counting the 0 before the decimal point (for example ...
616 views

You are given several pieces of paper which are as follows: (Unfortunately, a textual rendering is very difficult with this puzzle, so if someone can offer a suggestion on how to do it, that would be ...
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### How to solve Rubik's Cube using mathematical formulas? [closed]

I am trying to solve Rubik's Cube, but it took one month for me when I started. Are there any mathematical formulas, rules and tips for solving Rubik's Cube in less time (i.e. minutes)?
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### Make $\pi$ using 2 0 2 0 in this order

How can you make $\pi$ using 2, 0, 2, 0 in this order? Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, parentheses.
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### Painting a grid with 3 colours such that there are no right-angled triangles of one colour

What is the largest rectangular NxM grid (by area) that can be painted with 3 colours, such that no three cells of the same colour form a right-angled triangle. N and M must be 4 or greater. We only ...
180 views

### Find the value of $\bigstar$: Puzzle 10 - Uncertainty

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea, I recommend you solve Puzzle 1 ...
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### Find the value of $\bigstar$: Puzzle 9 - Options

This puzzle replaces all numbers with other symbols. Your job, as the title suggests, is to find what value fits in the place of $\bigstar$. To get the basic idea, I recommend you solve Puzzle 1 ...
213 views

### The Train and The Cyclist [closed]

A railway track runs parallel to a road until a bend brings the road to a level crossing. A cyclist rides to work along the road everyday at a constant speed of 12 miles per hour. He normally meets ...
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### Are all balls the same weight?

There are 10 balls which come in two possible weights. Using a balance scale at most 3 times, determine whether all the balls are the same weight or not. Notes: I got this riddle from this ...
286 views

### A 3x3 grid of numbers with unique row and column medians

Can you place every number from 1 to 9 into a 3x3 grid such that the median of every row and column is a unique value? The median of a row is the number that is greater than one number and smaller ...
194 views

### Ten, nine, eight, seven, six, five, four, three, two, one

Some of us already did, and some of us are going to end the years with the word "teen" in it soon, for another 94 years. So let me ask the question: How many distinct numbers can you produce with ...
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### Two dice with same probability for each sum mk2

Inspired by Two dice with the same probability for each sum? To cheat in a game of sums, you get yourself a pair of magic dice. That pair behaves in a wonderful way where each individual die is fair (...
253 views

### A 4x4 grid of numbers with unique row, column and diagonal ranges

Can you place every number from 1 to 16 into a 4x4 grid such that the range of every row, column and two main diagonals is a unique value? The range of a row is the difference between its maximum and ...
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### A Guide to the Number Rotation Puzzle

This is an extension of What is the strategy to solve Simon Tatham's Twiddle? in that it explicitly goes beyond the default gamemodes of Twiddle The Number Rotation Puzzle (NRP) is a combination ...
122 views

### A 3x3 grid of numbers with unique row and column ranges

Can you place every number from 1 to 9 into a 3x3 grid such that the range of every row and column is a unique value? The range of a row is the difference between its maximum and minimum values (...
51k views

### A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
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### Four dice puzzle: Postscriptum

This continues (and completes) the sequence of four dice puzzles: Four dice puzzle: 2,2,4,5 Four dice puzzle: What's the best throw? The days go by and Damiano is still throwing his four dice. He ...
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### Four dice puzzle: What's the best throw?

This continues Damiano's puzzle "Four dice puzzle: 2,2,4,5" Damiano keeps throwing his four dice. After a lot of throwing and thinking and working, he has determined for every throw $a,b,c,d$ of his ...
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### Four dice puzzle: 2,2,4,5

Damiano has thrown four dice and the numbers 2, 2, 4, 5 showed up on top. Damiano asks himself: What is the smallest positive integer that cannot be generated with these four numbers according to ...
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### Guessing the pattern: f(43)=13, f(79)=40,

I have these numbers and I couldn't guess the pattern of this question it might be easy or it might be hard whatever these are the numbers  f(43) = 13\\ f(79) = 40\\ f(111) = 120\\f(138)=161\\f(...
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### What part of maths covers Factory Balls?

There is this nice little game called Factory Balls. Playing it for 2 minutes (you can buy it on Steam or play for free on Kongregate) will probably give you a better overview of my screenshot example....
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### Four + Five = Nine

Obviously, FOUR + FIVE = NINE, but what if each letter is assigned a digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and two different letters can't be assigned the same digit? Fill in numbers for the ...
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### Which Numbers Replace the Question Marks?

Can you find out what the numbers below have in common? Can you figure out what comes next? ...
932 views

### Primes less than 100 in a 4 x 4 board

Place one of the digits (0 to 9) in each of the cells of a 4 x 4 board so that as many as possible of the 25 primes less than 100 divide at least one of the 10 positive 4-digit numbers that can be ...
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### 123456789 = 100 with three operations? [duplicate]

Given the sequence 123456789 You can insert three operations (+,-,X,/) into this sequence to make the equation = 100. Is there a way to solve this without brute force?
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### Happy birthday Ramanujan!

On December 22 2019, Ramanujan would have been 132 years old. In his memory here are two puzzles around 132. In the six vertices of each of these graphs place six positive integers that add up to ...
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### Don't touch my curve

What the heck is this? A zero, or not? Him after me, no more problem. Take the fourth and the fifth. You want some uniform? Take my test. But don't touch my curve. It's in one piece, ...
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### A famous dodecagon

A 12-sided polygon (Dodecagon) has the property, that neighbouring sides appear 4 times in a ratio of 1:1 and 8 times in a ratio of 7:6. Where can such a Dodecagon be found?
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### Creating 2020 in the fewest number of steps

You start with the number 1. You can create a new number by applying an operation on two existing numbers (can be the same). The operations are +, - and *. What is the fewest number of steps needed to ...