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.

Filter by
Sorted by
Tagged with
6
votes
1answer
51 views

Prime number snake (2)

This question is inspired by prime number snake. In the following grid, you have to place a number snake of numbers 1 to 100. Consecutive numbers have to go into neighboring cells. Numbers in grey ...
43
votes
5answers
3k views

Prime Number Snake

Place numbers 1 to 100 in the cells of the 10 x 10 board below in such a way that consecutive numbers occupy neighboring cells (either horizontally or vertically). Shaded cells should contain only ...
-4
votes
3answers
84 views

Previous palindrome date

2nd of February this year will be a palindrome date, because 02/02/2020 reads the same forwards and backwards. But when was the previous palindrome date?
10
votes
3answers
388 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 ...
-2
votes
1answer
67 views

Modular exponentiation. Why all different? [closed]

Why is it if we use 1 2 3 4 mod 5 and we take x^3 of this numbers, we come to: 1 3 2 4 (all numbers are different as you can see)
-3
votes
0answers
77 views

I love books and to read them and count them but I didn't have enough time! [closed]

So, I have ten books. My friend from Indonesia gave me ten and my friend from New York gave me 75. Then my sister took 4 but my brother got 1 back. Then I sold 15 to my friend from India and 5 to my ...
-1
votes
2answers
104 views

How to solve how many times the ball collides with the corner [closed]

In the cartesian coordinate system, four points (0, 0),(20, 0),(20, 19) and (0, 19) are used as vertices to draw a rectangle. At first, a ball with negligible size is at the (0, 0) point. It then ...
4
votes
1answer
330 views

Calculators are bad at Arithmetic

Consider the following fraction: 17/30 Punch this into a calculator and you'll get the following answer: 0.566666666666666666666666666667 However, I disagree. I say the answer is most ...
1
vote
3answers
1k views

The missing number

The integer numbers from 1-30 are mutually communicated to you one by one in a random order (one number about every 5 seconds). However exactly one of those numbers is not communicated. What is a ...
-2
votes
1answer
211 views

Locations on the Earth that are all separated by the same distance

What is the maximum number of distinct locations you can select on the surface of the Earth, such that the distance between every pair of locations is the same? Assume that the Earth is a perfect ...
18
votes
1answer
3k views

Is it possible to divide a square into convex pentagons?

I have seen this question on reddit (r/math's chatroom - to be specific). No one has answered it yet, so I thought I would pose the same question here. The only discovery I made that is worth ...
1
vote
4answers
285 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
votes
1answer
185 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
votes
4answers
888 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
votes
1answer
291 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
votes
1answer
278 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 ...
7
votes
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
votes
1answer
232 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
votes
1answer
224 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
votes
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
votes
3answers
315 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
votes
3answers
223 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
votes
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
votes
1answer
257 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
141 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
votes
2answers
439 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
votes
2answers
172 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
votes
1answer
167 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
189 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
617 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
votes
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
125 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
votes
1answer
64 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
181 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
votes
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
217 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
4k 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
288 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
201 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
154 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
254 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
854 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
124 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
52k 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
335 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
666 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
votes
5answers
756 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....