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.

Filter by
Sorted by
Tagged with
11
votes
4answers
975 views

Cover a square with three smaller squares

A square has a side length of 5 units. Is it possible to cover this square with three squares each with a side length of 4 units?
17
votes
2answers
254 views

Dominoroto-toto

Consider a domino tiling of a plane rectangle of size $n \times m$. (Obviously, at least one of $m$ and $n$ has to be even for that to be possible.) I personally hate those because they tend to look ...
10
votes
3answers
495 views

A packing game!

Amy and Ben are playing a game which is suggested by a genie. Amy first chooses $a,b,c\in\mathbb{R}^+$. Then a empty cuboid box with internal measurements $a+b,b+c,c+a$, and infinite supply of cuboid ...
8
votes
1answer
307 views

The Lucky Number

Lucky numbers are 4 digit numbers that have the following property: they are equal to the sum of the fourth power of their digits. Therefore, they can be expressed as follows: $$1000a+100b+10c+d = a^4+...
8
votes
1answer
278 views

A word becomes imaginary

I'm important in geometry If you add a letter, you get the German translation If you re-order the letters of the English word and add brackets () and multiply, it becomes imaginary If you re-order the ...
17
votes
1answer
191 views

Arithmetic Progression Sudoku

In this puzzle, each square must contain a positive integer. All rows, columns and boxes must contain an arithmetic progression of length 9. Good luck!
7
votes
3answers
262 views

Touching triangles at their vertices

What is the minimum number of non overlapping congruent triangles arranged in the plane, such that each vertex of the triangles coincide with exactly three triangles?
3
votes
2answers
177 views

Count the squares [closed]

My professor at college loves geometry and discrete mathematics. He gave us a question let see if you can solve it. He asked us ...
5
votes
4answers
316 views

A probably sunny Sunday

Besides this problem I also use the following one to rise the interest of my students on the Probabilities Theory. It's a funny puzzle were the use of simple arithmetic rules doesn't work. We have to ...
8
votes
1answer
300 views

The beginning of a factorial

Is there a positive integer n such that the decimal representation of n! starts with 123456789?
8
votes
1answer
321 views

Whose birthday is it?

A group of people have gathered for a birthday celebration. Their ages are related as follows: The product of the 1st person's and the 2nd person's ages is $311\frac{2}{3}$ plus the 3rd person's age. ...
12
votes
2answers
4k views

Move one digit to make the equation $62-63=1$ true

This mathematical statement is obviously false. Move one digit to make it true. $$62-63=1$$
7
votes
0answers
227 views

Sequence Puzzle - First Question of 42

Professor Tera was walking on Connecticut Road, where there are some public restrooms. Tera saw some students standing in a row. They seemed to be playing a game called Evolution. And it looked like ...
3
votes
2answers
127 views

Cube the digits and carry on

Take a number between 2001 and 2100 inclusive. Cube the digits of the number and add them together, then repeat the process with the new sum and restart the process over and over. For example if I ...
8
votes
8answers
2k views

How do you solve/understand this problem of who owes who?

There are people A,D,G,P "A" needs $2.50 from D,G,P "P" needs $2.50 from A,D,G ...
8
votes
2answers
370 views
+200

Modifying the puzzle: Cooperative hat-guessing, no mistakes, 3+ colors

Following Guess your hat color, but you don't have to and it's interpretation via Covering codes I tried to create a puzzle with more hat variativity, i.g. 3 types of hats. 4 hats are put on 4 ...
1
vote
2answers
118 views

Solve the magic square

My friend gave me the following magic square to solve $$\begin{bmatrix}\frac23&5&?\\\frac19&?&?\\?&?&?\end{bmatrix}$$ I can solve it. Can you? You must provide logical ...
4
votes
3answers
220 views

Cut the square cloth!

I have a square cloth with side length $x$ cm, and I am going to cut it into at least $n$ squares with side length $1$ cm for my customer, and also you cannot cut the cloth to thinner pieces (reminded ...
3
votes
0answers
92 views

Ideas on spatial puzzles for a city walk

Background. With the relaxation of covid-related restrictions, there was a need for intelligent city walks. Walk here is a moving between city objects by a certain (deterministic/stochastic) route. I ...
13
votes
3answers
753 views

Pythagorean triplets wheat field

A rectangular field has width $a$ and length $a+1$. We cut it into 3 triangles that all have integer side lengths. If all triangles have a different area, then what’s the minimum value of $a$? Please ...
4
votes
1answer
109 views

Sixty melons puzzle [duplicate]

Mohammad is a merchant working at the Rabat open-air market. As usual he met two wholesalers early in the morning: Farid gave him $30$ melons to be sold at the price of $1$ dirham for three melons. ...
2
votes
2answers
135 views

Calculation puzzle 012

What's A + B = ? I found A=60 and B=63x4=252, thus A+B=60+252=312; but, source says that's wrong answer. Source: This question was asked in YTU exam for int'l students in 2018. I have discussed about ...
0
votes
2answers
70 views

Calculation puzzle 010

Find the missing number in the sequence. 2 9 28 65 ? 217 Source: This question is taken from YTU YOS 2018 exam. I have mentioned them in other posts.
1
vote
1answer
68 views

Calculation puzzle 011

Find the missing number. ...
1
vote
1answer
108 views

A problem of Age

Recently I met a women which said: Do you know something funny? If you reverse my own age, the figures represent my husbands age. He is, of course, senior to me, and the difference between our age is $...
28
votes
4answers
6k views

Short but impossible math problem

Given these four equations/inequalities: 1x=2 2x=4 3x=3 4x>8 What is x?
5
votes
2answers
321 views

Seventeen positive integers

Find 17 positive integers such that no four of them have, pairwise, a common divisor greater than 1, but, likewise, no four of them are, pairwise, relatively prime. Do so in such a way that the ...
3
votes
0answers
137 views

The madness of a master

It was midnight. Mr. Holmes was suffering from abdominal pain, shortness of breath, pain in the bones, skin lesions and whatnot? So in this condition, why would Mr. Holmes drive to Brazilian Churches, ...
3
votes
4answers
613 views

What are the fewest weights you need to balance any weight from a triangular seesaw?

I saw this question: What's the fewest weights you need to balance any weight from 1 to 40 pounds? Suppose you want to create a set of weights so that any object with an integer weight from 1 to ...
3
votes
2answers
138 views

The number game

There is a number, the second digit of which is smaller than the first digit by $4$, and if the number was divided by the digits' sum, the quotient would be $7$. What is this number.
1
vote
2answers
93 views

The date $8.8.6.4$

The date $8.8.64$, meaning August $8, \; 1964$ is a very interesting date, because the product first $2$ numbers equals the third. Can you find the year of the twentieth century which gives the ...
2
votes
1answer
67 views

$3$ quart from $10$, $5$ and $4$ quart

Mr.Affison had two $10$ quart containers full of wine. He also had a $5$ quart and $4$ quart measurement. All he wanted to do was to put exactly $3$ quarts into $2$ of his measurements.}Now he was ...
6
votes
4answers
427 views

Maximum amount of the Letter-Number-game

There is a number-game which you play like this: You think of a number eg. $8$. Then think: How many letters does this number have? In our example: $5$ And now do step one with $5$ This goes on ...
6
votes
5answers
475 views

All wrapped in functions

Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f(x)f\big(f(x)+y\big)=f\big(x^2\big)+f(xy)$$ for all $x,y\in\mathbb R$ Problem by me Most elegant solution wins!
11
votes
2answers
330 views

My identity in high school

My first semester—no, my entire freshman year—in high school, I was all alone. As I started my sophomore year, I finally made a friend. Two, actually. They weren't in the same class as me, but for the ...
5
votes
1answer
134 views

An unexpected ratio of an integer

If $\frac{1}{4}$ of 20 is equal to 6, what is $\frac{1}{3}$ of 10?
5
votes
11answers
6k views

In what field does π²=2?

In what field does $\pi^2=2$, where $π$ is the ratio of the circumference of a circle to its diameter? Remember to think outside the box and that I am looking for a complete answer. Hint:
5
votes
1answer
88 views

The sandpiles on the beach

We call a convex polyhedron a sandpile if one of the faces, called base, has a common edge with all the other faces. Furthermore, each vertex is linked with three edges. We consider the sandpiles by ...
2
votes
1answer
104 views

En-lighting math puzzle [duplicate]

1 + 1 =1 2 + 6 =8 3 + 1 =3 4 + 5 =9 5 + 5 =5 6 + 0 =8 7 + 8 =8 8 - 1 =E
5
votes
3answers
1k views

Math problem: 1+1=0 [duplicate]

See if you can solve this math-problem: $$ \begin{bmatrix} 1&+&1&=&0\\ 2&+&8&=&2\\ 2&+&2&=&0\\ 9&+&8&=&3\\ 3&+&4&=&0\\ 6&...
1
vote
0answers
94 views

Searching online catalogs is a pain. Can you tell me if it's worth my trouble?

Searching online catalogs is a pain. Can you tell me if it's worth my trouble? As an example, I searched the following online catalog of a well-known country-wide British outlet for the keyword "...
3
votes
1answer
94 views

Number of children

Here comes an easy one: A Family has several children. Each brother has the same numbers of brothers and sisters, but each sister has twice as many brothers as sisters How many sisters and brothers ...
14
votes
3answers
2k views

Ten miles south, east, north and west

I'm standing on the surface of the Earth. I walk ten miles south, ten miles east, ten miles north and ten miles west. I end up exactly where I started. Where on earth am I?
-4
votes
3answers
100 views

Math Question! Can u solve it? [closed]

This took me 25 seconds! How long did it take you? 11 X 11 = 4 22 X 22 = 16 33 X 33 = ??? The answer is right in front of you so do not think in normal math rules!
20
votes
6answers
2k views

Size of a square in a square

Given a unit square (blue in the picture), pick a point on one edge and label it A. Label the distance from the nearest corner to A as x. Pick one of the corners opposite A and label it B. Call the ...
4
votes
2answers
148 views

A Pleasant Dinner Party Conversation

I used to be single, dig it? Then I found someone else who was single, and now we're in a relationship. The thing about relationships is that it's more than the sum, or even the multiple, of its parts....
8
votes
3answers
448 views

Guess your hat color, but you don't have to

Here is the puzzle: N hats are put on N logicians, each hat color is selected randomly: black or white. As usual, every logician doesn't see the hat on his own head, but sees the rest. They cannot ...
35
votes
12answers
9k views

Ten girls around a table

Ten girls are sitting around a table. Each of them picks a real number and whispers it to the two neighbors immediately to the left and to the right. (Hence: each girl communicates one number, and ...
6
votes
3answers
289 views

Extended face-planes of an Octahedron

When extending the face-planes of a regular Octahedron, how many cells (bounded and unbounded) are formed in space?
10
votes
1answer
460 views

Mathematics in adolescence

When I start to teach probabilities, I challenge my students with the following: Thelma is 16 years old and can only go out at night if one of her parents gives her permission. She knows her father ...

1
2 3 4 5
65