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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2
votes
2answers
97 views

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 $3$ ...
4
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1answer
148 views

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.
10
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4answers
850 views

Making the whole set into primes

Let's say you start with a set of sequential integers starting from 2, so: $ 2, 3, 4, 5, \dots, N $ for some $ N > 2. $ The goal is to use identical basic arithmetic operations ($ +, -, \times, \...
6
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2answers
281 views

Building the perfect number 28 with fractions

You are given the fractions $\frac{4}{3}, \frac{7}{3}, \frac{10}{3}, \frac{13}{3}.$ Use any operation of $+, -, *, /, ()$ to build 28 with those four fractions. You must use all four fractions ...
7
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1answer
270 views

Building the perfect number 28 with fractions - part2

Here is a follow up of Building the perfect number 28 with fractions You are given the fractions $\frac{3}{2}, \frac{5}{2}, \frac{7}{2}, \frac{11}{2}.$ Use any operation of $+, -, *, /, ()$ to build ...
9
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1answer
243 views

The seven letter word

Don't worry, I won't let you overflow. Is anyone operating on you? I won't let you overflow by that. Do you want to link yourself? I won't let you overflow by that. Is there an ...
7
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9answers
3k views

Creating 123456 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 ...
6
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1answer
219 views

A new year's mathematical mystery

Sam, Magnus, and Olivia each try to write the number 2020 as the sum of consecutive positive integers. They each use more than one integer, a different number of integers to the others, and none of ...
8
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1answer
221 views

How much information can we get from a thermometer?

A fairly common Sudoku variant is so called "Thermometer" Sudoku. In this variant arrows with a rounded end (which look like a thermometer) are added to the grid, with the rule that the numbers on ...
29
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6answers
5k views

A robot surviving on top of a 3x3 platform

A robot sits in the central square on top of a 3x3 platform. The robot can move up, down, left or right, but if it steps off the platform it will crash and die. You can preprogram the robot to make a ...
10
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3answers
314 views

What is the largest number of cubes that can be cut?

Consider a cube made up of 27 unit cubes. If you consider a plane going through the middle of the larger cube it cuts through a number of the unit cubes. The number of cubes that are cut depends on ...
4
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3answers
219 views

Linking Cars on a Track going at Different Speeds

A kid places three model cars on a long, straight track equally spaced apart. He sets each of them to a different speed (though he forgot the specific speeds). These cars are special, though: they ...
3
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6answers
1k views

Make 28 with the numbers 2020

Try to make 28 from the numbers 2020. Allowed operations: +, -, x, ÷, ! (factorial), exponentiation, square root, squaring, parentheses.
8
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1answer
247 views

Is Every Obtuse Angle A Right Angle?

The Journal of Irreproducible Results once posted an article saying that every obtuse angle is a right angle. Their argument follows below: Given the obtuse angle $x$, we make a quadrilateral $ABCD$ ...
3
votes
1answer
136 views

Guess the missing digits [duplicate]

Can you guess the missing digits in the following multiplication? ??? x 3? = ???? Digits from 1 to 9 appear exactly once each. The goal is to solve it with as little calculation as possible.
12
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2answers
438 views

Freddy Krueger's Lullaby

1, 2. Freddy is drawing eyeballs. 2½, 3. One iris got bigger. 3½, 4. The other got bigger. 5, 6. Aura passes from and to irises. [NUMBERS REDACTED] Never ...
2
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2answers
167 views

Make numbers 1-50 using $\pi$ and its digits (but with some penalties) [closed]

In this problem, you will be allowed to use some operations and additional digits from the basic approximation of $\pi=3.14$ having some penalties, as follows: Operations: Using basic operations and ...
7
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1answer
158 views

Removing a Point, then Adding Two Others

Start with a point on $(0,0)$ on a two-dimensional lattice. Every move, you must follow this rule: for a point $(m,n)$, if there are no points on $(m+1,n)$ or on $(m,n+1)$, then you can remove point $(...
3
votes
1answer
184 views

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 ...
5
votes
1answer
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 ...
8
votes
3answers
616 views

Discover the six-character password!

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 ...
-1
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1answer
2k views

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)?
2
votes
1answer
121 views

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.
-1
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1answer
63 views

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 ...
6
votes
3answers
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 ...
2
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1answer
265 views

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 ...
6
votes
2answers
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 ...
29
votes
7answers
3k views

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 ...
3
votes
3answers
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 ...
-4
votes
3answers
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 ...
2
votes
1answer
152 views

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 (...
6
votes
2answers
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 ...
10
votes
2answers
833 views

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 ...
4
votes
2answers
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 (...
67
votes
12answers
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 ...
3
votes
1answer
333 views

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 ...
9
votes
1answer
391 views

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 ...
8
votes
2answers
665 views

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 ...
9
votes
3answers
3k views

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(...
13
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5answers
746 views

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....
14
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5answers
3k views

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 ...
5
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2answers
706 views

Which Numbers Replace the Question Marks?

Can you find out what the numbers below have in common? Can you figure out what comes next? ...
18
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5answers
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 ...
-2
votes
1answer
103 views

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?
13
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2answers
263 views

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 ...
2
votes
1answer
142 views

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, ...
9
votes
1answer
586 views

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?
20
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10answers
5k views

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 ...
9
votes
1answer
224 views

Missing number puzzle: how to get this answer?

Today I went to pick up my daughter from school before the start of the winter holidays. I found her chatting with her teacher and they presented me with a little math puzzle. It was on a card from a ...
15
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9answers
4k views

Three people wearing hats

Ms. Doha gave hats with different non-zero single digits (two of which are factors of the third) to Ms. Haha, Ms. Lola and Mr. Hehe. The three of them can't see the digits on their own hat though they ...