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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7
votes
2answers
723 views

Paint numbers from 1 to 23 with three colours

Can you paint every number from 1 to 23 with three colours, such that there are no distinct numbers $𝑎,𝑏,𝑐$ of the same colour with $𝑎+𝑏=𝑐$? For example, you cannot have 2, 3 and 5 of the same ...
5
votes
1answer
426 views

Paint numbers from 1 to 8 with two colours

Can you paint every number from 1 to 8 with two colours, such that there are no distinct numbers $a, b, c$ of the same colour with $a+b=c$? For example, you cannot have 2, 3 and 5 of the same colour ...
6
votes
1answer
216 views

Identify the odd one out element

There are two columns (two sets), in each set there is a pattern among the 7 elements. The elements are not arranged in any order, the two patterns are not necessarily the same, but they are related ...
1
vote
1answer
107 views

Last Person Remaining Avoids Death [duplicate]

There are 1600 people sitting around a circular table. The first person (person 1) has a sword and kills the second person then hands it to the next alive person (in this case person 3). Person 3 ...
6
votes
3answers
644 views

Number Equation Matrix

Can somebody please solve this? My daughter's school teacher gave her this puzzle to solve at home. But to me it seems a little out of order, and that's why I am asking here for help.
4
votes
2answers
171 views

Covering an 8x8 grid with W pentominoes

What is the minimum number of W pentominoes you need to cover every cell of an 8x8 grid? Pentominoes may overlap each other and sit outside the boundary of the grid. They can also be rotated in any ...
14
votes
6answers
2k views

Covering an 8x8 grid with X pentominoes

What is the minimum number of X pentominoes you need to cover every cell of an 8x8 grid? Pentominoes may overlap each other and sit outside the boundary of the grid. An X pentomino looks like this:
0
votes
4answers
136 views

Rectangles formed from every tetromino, tromino and domino

Can you form a 4x7 rectangle from every tetromino, tromino and domino? There are 5 different tetrominoes, 2 trominoes and 1 domino. Can you find different arrangements that are not mirrors/rotations ...
16
votes
1answer
1k views

Find d this ones stumped me help?

This one is annoying me so much. Got this from a maths teacher.
0
votes
1answer
191 views

A town E miles away?

I got this from my maths teacher What is the value of 'E'?
6
votes
2answers
484 views

10x10 grid with no unpainted hexominoes

What is the smallest number of cells you need to paint in an 10x10 grid, such that it contains no unpainted hexominoes? Note that a hexomino is a set of 6 adjacent cells (horizontally or vertically). ...
4
votes
2answers
388 views

8x8 grid with no unpainted pentominoes

What is the smallest number of cells you need to paint in an 8x8 grid, such that it contains no unpainted pentominoes? Can you find multiple solutions? Note that a pentomino is a set of 5 adjacent ...
3
votes
2answers
205 views

10x10 divided into the most number of rectangles of different area

How can a 10x10 be divided into rectangles such that there are as many as possible and they all have different area? Can you find multiple solutions that are not mirror/rotation of each other? Good ...
0
votes
1answer
57 views

7x13 rectangle divided into 13 different rectangles

Can you divide a 7x13 rectangle into 13 rectangles all of different area? Can you find multiple solutions? Note that rotations and mirrors don't count as separate solutions. Here is a similar puzzle ...
0
votes
3answers
82 views

4x7 rectangle divided into 7 different rectangles

Can you divide a 4x7 rectangle into 7 rectangles all of different area? Can you find multiple solutions? Good luck! P.S. @Deusovi wanted me to make puzzles that have an "aha moment", so here is my ...
4
votes
1answer
157 views

Prime magic star

Can you replace the letters with 10 consecutive primes such that the sum of numbers on each line is equal? I expect this to be solved with a computer. Good luck!
3
votes
1answer
150 views

Partition a 3x3 square into rectangles [closed]

Yesterday I watched "The man who knew infinity" about the amazing Ramanujan. Inspired by the partitions problem from the movie I came up with a puzzle: In how many ways can you partition a 3x3 grid ...
5
votes
3answers
209 views

Rawrdon Mamsay pays a visit

Now, I should warn you, this is one of my practical problems; meaning I don't know the solution and the answer's probably anticlimactic (like this or that). Still... My old pal Rawrdon Mamsay is soon ...
8
votes
1answer
650 views

A curious 5x5 square

Can you fill a 5x5 grid with numbers from 1 to 5, such that every number occurs exactly once in each row, exactly once in each column and exactly once in each broken diagonal (in both directions)? ...
0
votes
2answers
103 views

Painting edges of a 3x3 grid with 4 colours

Can you paint the edges of a 3x3 grid with 4 colours, such that: The colours of edges of every 1x1 square are different. The colours of edges adjacent to every vertex are different. Here is a ...
0
votes
1answer
64 views

Painting edges of a 2x2 grid with 4 colours

Can you paint the edges of a 2x2 grid with 4 colours, such that: The colours of edges of every 1x1 square are different. The colours of edges adjacent to every vertex are different. Good luck!
8
votes
0answers
151 views

The Flippin' Magician's 7-card Grand Finale

This question is a followup to this question by @ais523, which itself was a followup to this question by @Wen1now. After touring the globe to accolades when performing his 10-card trick and 8-card ...
3
votes
2answers
186 views

Cross the pond, but there's a catch!

There is a square pond, conveniently divided into segments, with coordinate $(0,0)$ in the bottom left and $(10,10)$ is the top right. You have planks length $2$ and $3$. You start at $(0,0)$ and ...
15
votes
3answers
1k views

Transferring 9 pegs on a 9x9 grid

You are given a 9x9 grid with a set of 9 pegs (red circles) arranged in a 3x3 pattern in the corner, as shown below: A peg can jump over another adjacent peg in any direction (horizontal, vertical or ...
37
votes
1answer
7k views

I'm largest when I'm five, what am I?

I'm very common and often you see me, Everything's believed to be made of me. Make no mistake, I look largest when I'm seven, But I'm largest when I'm five, it is proven. But alas at ...
10
votes
1answer
370 views

Fill the Image Sequence Ep. 2

Suggested by Athin, try & make another feasible puzzle for this series. Enjoy :D The prologue also be revised more precisely. This puzzle will provide several images. These images compose a ...
4
votes
2answers
230 views

Primes from arithmetic and geometric progressions

The five primes, 131, 157, 211, 349, 739, are neither in arithmetic or geometric progression, but are instead the sum of the corresponding terms of two progressions of five terms each, one arithmetic ...
5
votes
1answer
313 views

Consecutive numbers that are Manhattan distance 5 apart

Can you place numbers from 1 to 36 on a 6x6 grid, such that the distance between any two consecutive numbers ($a$ and $a+1$) is Manhattan distance 5? Bonus question: can you also make 1 and 36 be ...
12
votes
4answers
2k views

Consecutive numbers that are Manhattan distance 3 apart

Can you place numbers from 1 to 16 on a 4x4 grid, such that the distance between any two consecutive numbers ($a$ and $a+1$) is Manhattan distance 3? Bonus question: can you also make 1 and 16 be ...
1
vote
2answers
142 views

Painting a 6x6 with 3 colours

Can you paint a 6x6 grid in red, green and blue, such that its every 3x3 sub-grid contains exactly 5 red, 3 green and 1 blue cell? Good luck!
8
votes
4answers
1k views

3x3 self-descriptive squares

A self-descriptive square is a square grid filled with integers such that: The sum of the numbers in any row describes the number of times that row’s rightmost number appears in the square. The sum ...
-9
votes
4answers
280 views

It's his birthday!

A friend of mine told me that he was about to have his birthday. However, he didn't tell me what his birthday was. When is his birthday? Compulsory Hint 0 Compulsory Hint 1
5
votes
1answer
472 views

No interest ever. Just a fee for my end,

Need to lend a tenner? No interest ever. Just a fee for my end, A third of what I lend. Falling short of the fee? I will lend it to thee! What do I lend you all together?
-5
votes
4answers
253 views

computer programmer's maths puzzle [closed]

A computer programmer looked at part of his code x = x + 1; and then thought what a strange equation that would be for a mathematician $$x=x+1$$ The programmer ...
17
votes
5answers
1k views

Generating Roman numerals with dice

This puzzle is closely based on this one: Generating numbers with cubes Now we want to generate Roman numerals by placing up to three 6-sided dice side by side. We are allowed to write multiple ...
1
vote
0answers
80 views

What are my sisters' ages? (With ice cream!) [duplicate]

This is from a book I read as a child. Steve said to his friend Jessica, "I have 3 sisters. The sum of their ages is the same as my age, and the product of their ages is 36. How old are my sisters?"...
13
votes
5answers
2k views

Generating numbers with cubes

I saw an interesting calendar in a shop. It is composed of two cubes with numbers written on their 6 sides. By placing these cubes side by side one can make any day of the month from 1 to 31 (even 32)....
7
votes
2answers
427 views

Smallest prime number which when spelt out contains the letters P, R, I, M, E

So inspired by recent slew of questions based on prime numbers. What is the smallest prime number when written out (Using the Western numbering system and English) would you encounter the letters P, ...
1
vote
1answer
140 views

Minesweeper-type puzzle

The premise is simple. We get a n*n matrix with numbers ranging from 0 to 16. The matrix is the result of a minesweeper-kind of addition whereby we have an original matrix containing numbers ranging ...
0
votes
1answer
71 views

TripTog's problem with his socks [closed]

Our friendly three-footed alien TripTog has two triplets of socks, which he keeps in a drawer in a room. Each triplet of socks is labeled 1, 2 or 3, because TripTog is very meticulous about which ...
7
votes
3answers
792 views

Paint 10 cells of a 10x10 grid

Can you paint 10 cells of a 10x10 grid such that the largest unpainted rectangle has area of 10 cells? Here is a similar question for the 7x7 grid: Paint 7 cells of a 7x7 grid Good luck!
5
votes
2answers
534 views

Paint 7 cells of a 7x7 grid

Can you paint 7 cells of a 7x7 grid such that the largest unpainted rectangle has area of 6 cells? Good luck!
1
vote
0answers
35 views

Triangle of numbers [duplicate]

You can place each number from 1 to 10 into a triangle, such that each number below the first row is the absolute difference of the two numbers above it: ...
1
vote
1answer
85 views

Neighbouring numbers summing to a prime on a 4x4

Can you place every number from 1 to 16 on a 4x4 grid such that every pair of neighbouring (horizontally and vertically) numbers sum to a prime? Note that the generated primes can be reused. A ...
-2
votes
1answer
93 views

Distance between two friends [closed]

Two friends are 200 meters apart in a concourse. They then both walk 100 meters each with their faces towards to each other. Yet after this 100 meter walk they are still 200 meters apart.
4
votes
1answer
132 views

“Short” And Sweet Math

In the following chess diagram, how many possible chess postions exist? No looking at the solution! Source: P1359129 & Andrew Jonathan Mestel, Retros mailing list, 2/1/2019
4
votes
1answer
163 views

Find the least expense?

You want to build a shop between three roads in the shape of an equilateral triangle. What would be the best location for the shop so that you can reach each road with the minimum transportation ...
4
votes
3answers
488 views

Neighbouring numbers summing to a prime on a 3x3

Can you place distinct numbers from 0 to 9 on a 3x3 grid such that every pair of neighbouring (horizontally and vertically) numbers sum to a prime? Can you find multiple solutions? Note that the ...
1
vote
1answer
93 views

One-digit products in a row of numbers, base-N

Generalizing One-digit products in a row of numbers to base-N: For which bases N does there exist at least one solution to the following: "The digits from 1 to N can be arranged in a row, such that ...
17
votes
4answers
3k views

Smallest PRIME containing the first 11 primes as sub-strings

In Smallest number containing the first 11 primes as sub-strings, @Alconja successfully found the smallest number which contains the first eleven primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31) as ...