# 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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7answers
995 views

### To equip hand sanitizers

There was an event held by a group. In this COVID-19 era, there were many hardships in equipping quarantine supplies, in addition to carrying out the event. Several bottles of the same hand sanitizer ...
3answers
422 views

### Two integer sided equilateral triangles with integer distances

In this figure with two non-congruent equilateral triangles and three-fold rotational symmetry the distance between any two of the 6 vertices is an integer. Can you give a solution? I know only one ...
2answers
196 views

### Determine minimal number of moves to find cells on a square table 10×10 in which a treasure is hidden

In a 10x10 square table, two neigbouring 1x1 cells contain a hidden treasure. John needs to guess these cells. In one move he can choose some cell of the table and can get information whether there is ...
1answer
35 views

### A rectangle with non-integer side lengths [duplicate]

Is it possible to build a gapless rectangle with non-integer side lengths using rectangles each with two integer side length and two non-integer side length? The rectangles are not required to be the ...
2answers
491 views

1answer
122 views

### Heptagon, nonagon

What is the trick to constructing a heptagon and a nonagon which have all their sides equal? The length of the side has to be a natural number. Your answer should include a drawing of the two polygons....
2answers
281 views

### Cutting a shape into two equal area shapes

Given the following shape - an hexagon ABCDEF of which a parallelogram CDGH is cut out. With a single cut divide the shape into two equal area shapes by means of an unmarked . You may draw lines and ...
3answers
90 views

### 5x5 grid with no tetrominoes containing repeating colors

Paint the cells of a 5x5 grid with 𝑛 colors, such that every possible tetromino found in the grid uses 4 different colors. What is the smallest value of 𝑛 possible in such a coloring? Here is a ...
3answers
356 views

### 4x4 grid with no trominoes containing repeating colors

Paint the cells of a 4x4 grid with 𝑛 colors, such that every possible tromino found in the grid uses 3 different colors. What is the smallest value of 𝑛 possible in such a coloring?
2answers
103 views

### A number built with two-digit primes

What is the largest number, which can built as a sequence (from left to right) of different two-digit primes only? For example, 1371731 is valid, 137131 is invalid (containing 13 twice), 139717 is ...
1answer
670 views

### Finding the median of 5 numbers

There are 5 boxes labeled A, B, C, D and E. Each box contains a distinct number, but you don't know what it is. You can select three boxes and the Oracle will tell you which box contains the median* ...
3answers
570 views

### Table of mathematical expressions - fill in 1-9

Fill in the numbers 1 through 9 in the 9 empty cells (each number appears exactly once) to make the row and column expressions equal to the number at the end of the row or column. Regular math ...
2answers
94 views

### A triangle inside a triangle

All sides of a triangle T1 are shorter than the shortest side of a triangle T2. Is it always possible to put triangle T1 completely inside triangle T2?
1answer
97 views

### Gaby's 21 students sitting around a circle [closed]

Gaby numbers her 21 students with the primes between 11 and 97. She now asks them to sit around a circle making sure that any two of them sitting next to each other have either their tens or units ...
1answer
105 views

### How to open the lock from this safe?

The puzzle is as follows: The figure from below shows a lock mechanism used to store sensitive data microfilms from a certain lab. This mechanism is magnetic and consists in numbered buttons which ...
2answers
460 views

### How to fill 1/3 of the cylinder?

You are given 3 containers - pictured in this order below: a box with side 2, height 1, and a cone with base radius 1 and height 1 in the middle. a box with side 2, height 1, and a half sphere with ...
2answers
263 views

### Pandigital fraction sum that evaluates to 1

Fill in the nine X spots in the following equation using each of 1, 2, ..., 9 exactly once, so that the equation is satisfied. The XX in the denominator denotes concatenation of two digits.  \frac{X}...
2answers
83 views

### A challenge to make 1 - 100 [closed]

So this challenge is you have (don't have to) make the numbers 1 - 100 by using the numbers 1, 3, 4, 6 only once. I'm stuck on how to make 54. Can anyone help me? P. S. You can use +, -, ÷, x, ! And ...
1answer
119 views

### How many 𝑛-digit integers have the property that the block of its first 𝑘 digits is a prime or divisible by 𝑘 for all 1 ≤ 𝑘 ≤ 𝑛?

Are there infinitely many integers with the property that the block of its first 𝑘 digits (for all 𝑘, 1 ≤ 𝑘 ≤ 𝑛, where 𝑛 is the number of its digits) is either a prime number or is divisible by 𝑘...
4answers
596 views

### Divided by Pie Squared. Aaahhh

I have a machine that can divide a square pie into 9 equal square pieces using 4 blades: The blades can be moved, but there is only one control - which defines the width of the blades in both ...
2answers
310 views

### Four touching circles

Three identical circles are placed such that they touch each other. A larger circle is drawn around the smaller circles such that it touches them, as shown in the diagram. Can you find the ratio ...
4answers
552 views

### 8x8 square with no adjacent numbers summing to a prime

Can you fill a 8x8 grid with numbers from 1 to 8 such that: Every number occurs exactly once in each row and in each column (Latin square). No two adjacent (horizontally or vertically) numbers sum to ...
1answer
70 views

### 4x4 square with no increasing triples

Can you fill a 4x4 grid with numbers from 1 to 4 such that: Every number occurs exactly once in each row and in each column (Latin square). No row or column contains 3 adjacent numbers that are all ...
2answers
1k views

### Not so random walk

I'm out for a very long walk, and I’m bored, so I decide to walk in a mathematical way. The first image shows the first 500 steps, and the second image is my path after 50000 steps. The colors are ...