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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2
votes
1answer
45 views

Fetching Alchemist IV

This is the fourth puzzle in the Fetching Alchemist series, and is another puzzle that is exclusive to Puzzling SE until solved. This one might be a little too easy for those of you who have already ...
2
votes
0answers
61 views

Connect the dots to form a polygon

a) In each of these two grids of dots, 5 x 7 and 7 x 9, connect all of them so as to form polygons of 35 and 63 sides respectively (two consecutive segments can therefore not be collinear as they ...
11
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3answers
465 views

Even odds from die with single mark

We want to make a close equivalent of a fair coin throw, by throwing an N-sided fair die T times. The catch: only one side is marked, by a colored disk on that side's center (like the traditional ...
17
votes
9answers
324 views

Clever or interesting or elegant or beautiful ways to write “80” [closed]

A wonderful friend who is a maths professor, is turning 80 next month. He's just published his 22nd math textbook! [Prof John Vince.... his books are about math for computer graphics] I would love to ...
3
votes
1answer
104 views

Fetching Alchemist III

This is the third puzzle in the Fetching Alchemist series, and I am experimenting with a new format here. This time, I won't tell you in advance what the perfect score is. The first guess may be ...
0
votes
2answers
100 views

Tessellation with nonagons and equilateral triangles

What type of convex nonagon is required to tesselate a plane with equilateral triangles and nonagons? All sides of the nonagons are equal. NOTE: Partial tessellation of a plane should accompany your ...
3
votes
1answer
118 views

Fetching Alchemist II

This is a puzzle from the Expert section of my game Fetching Alchemist, visually modified for presentation here. It is a variant of the Travelling Salesman problem where you are trying to complete a ...
5
votes
3answers
482 views

Another puzzle with area

Squares $ABCD, DCGH, BEFG$ and $ELKM$ are positioned as shown on the picture. Find the area of triangle $DGK$ if you know that the area of square $ABCD$ is $20$.
8
votes
1answer
144 views

Puzzle with the point inside paralelogram and area

We have a paralelogram $ABCD$ and point $P$ inside it. Halflines $BP$ and $DP$ cuts respectively lines $AD$ and $AB$ at $E$ and $F$. Why are the area of $ABPD$ and $CEPF$ the same regardles of the ...
-5
votes
1answer
86 views

How to solve this equation [closed]

$$ {2\over x-14}+ {5\over x-11} = {5\over x-13}+ {2\over x-9}$$ It is puzzling me for a days. I'm getting huge polynomial I don't like.
7
votes
2answers
174 views

Adding coins inside a ring of coins

17 identical coins with diameter 1 are lying flat on a table, such that their midpoints build the vertices of a regular 17-gon (regular heptadecagon) and adjacent coins touch each other. What is the ...
-2
votes
0answers
51 views

How many times they should journey? [closed]

In a Colony, there are men, women and children. 4 women can carry as much as water as 7 children. 3 men can carry as much as 2 women and 1 child combined. If 7 men, 15 women and 4 children each visit ...
2
votes
1answer
137 views

Fetching Alchemist I

This is a puzzle from the Expert section of my game Fetching Alchemist, visually modified for presentation here. It is a variant of the Travelling Salesman problem where you are trying to complete a ...
9
votes
1answer
702 views

Who will win in a game of writing 3 consecutive Xs on a 2022 × 1 board?

Ana and Bob alternately write Xs on a 2022 × 1 board. The winner is the one who makes 3 consecutive Xs. Who has the winning strategy if Ana plays the first move? Describe such a strategy.
3
votes
1answer
99 views

Snake game on a 9×9 grid

You are playing a snake game. The snake starts in the top-left corner of a grid. Each cell of the grid is either empty or a wall. Each turn you can press a key to move the snake in one of four ...
2
votes
1answer
81 views

Snake game on a 6×6 grid

You are playing a snake game. The snake starts in the top-left corner of a grid. Each cell of the grid is either empty or a wall. Each turn you can press a key to move the snake in one of four ...
22
votes
4answers
2k views

Which die should you choose?

You are playing a game with dice. You have a grid with 13 cells shown below. A token starts in the left-most cell (start). Each turn you roll an $n$-sided die and get a number $x$ between $1$ and $n$, ...
-5
votes
0answers
43 views

Mathematics based question [duplicate]

Vani meam has three Tatva books, one for chemistry, physics and biology. The chemistry book had 120 pages, the physics book has 10% more pages and the biology book has 10% fewer pages. In a class, she ...
4
votes
2answers
279 views

Finding the root of a basic sequence

The sequence starts with the following: a1 = 1, a2 = 2, a3 = 5, a4 = 4, a5 = 6, a6 = 10, a7 = 9, a8 = 8, a9 = 21, a10 = 12, a11 = 13, a12 = 20, a13 = 33, a14 = 15, a15 = 42, a16 = 16, a17 = 19, a18 = ...
-6
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0answers
84 views

Difficult question .. Plzzzz solve this question [closed]

It's question image plzz answer this question Very difficult question
0
votes
1answer
99 views

Your typical math sequence

1, 2, 16, 4, 16, 16, 52, ?, 52, 16, 52, ?, 40, 52, ? What are these question marks? a) 8, 16, 160 b) 16, 8, 190 c) 52, 16, 160 d) 8, 25, 90 e) Impossible to determine
-1
votes
0answers
92 views

card(N) != card(N) [closed]

The link below connects to a proof with an error in it. Identify the step(s) where the error occurs, and describe why the step(s) is/are wrong. Proof containing error [1] If there is a bijection ...
5
votes
3answers
163 views

Numbers with minimal sum at the vertices of a cube

The eight vertices of a cube are marked with numbers from 1 to 8 such that the sum of any three numbers on any face is not less than 10. What is the minimum sum of the four numbers on a face?
3
votes
0answers
150 views

One vs many. Can white force a draw?

On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
-2
votes
0answers
53 views

General aptitude question [duplicate]

Thomas bought a train set with 25 toy engines that run at different speeds. The train set has five parallel tracks that can be built to race the engines. After each round, Thomas notes down the ...
7
votes
2answers
259 views

Can the fugitive escape?

A fugitive is surrounded by N police officers, with the nearest one at distance 1 away. The fugitive and the officers move alternatively. In a fugitive move, the fugitive can travel no more than a ...
4
votes
1answer
64 views

A 4x6 grid with adjacent integers with gcd > 1

You are given a 4x6 square grid. Each square of the grid should be filled with different positive integers. The gcd (greatest common divisor) of any two adjacent (horizontally or vertically) squares ...
4
votes
1answer
113 views

Is it possible to calculate group 3's factor of 3 in Thistlethwaite algorithm?

https://www.jaapsch.net/puzzles/thistle.htm I'm trying to generate 29400 ($8C4^2 * 6$) indices for each one of the cube states in G2. $8C4^2$ = 4900 is for solving the corner and edge pieces (forming ...
-2
votes
1answer
147 views

Get a expensive donut for 75% off! [closed]

You are going to a donut store, which donuts are more than 500 dollars. The most fancy one is the Donut Dedeluxe, which cost 5000 dollars. Luckily, they have a 75% off which is now 1,250. But, you ...
3
votes
3answers
246 views

Not selling 100 pencils

A shop sells pencils only in boxes of fixed size. It cannot sell 100 pencils. It can sell any larger amount of pencils. It has one of each size box on display. question 1: What is the minimum amount ...
1
vote
1answer
120 views

What is the greatest number of pencils that you cannot buy? [duplicate]

A shop sells pencils in boxes of 31 and 38. What’s the highest number of pencils a person cannot buy? In general, if the shop is selling pencils in boxes of p and q, then what is the highest number ...
9
votes
1answer
913 views

My grandfather's coins

When my grandfather died, he left his fine collection of coins, not more than 2500 of them, to his children, a different number to each of them, and in decreasing amounts according to their ages. To ...
6
votes
5answers
331 views

Reducing $\pi$ to zero

You are given the first 20 digits of $\pi$: 31415926535897932384. In each move, you can select a contiguous group of digits and increase/decrease them all by the same integer, provided that each ...
11
votes
3answers
337 views

Inhomogeneous circle packing

In the figure, what is the diameter of the smallest circle assuming the two parallel lines are one unit apart? Note: There is at least one elegant, geometric proof. Attribution: Mine, but wouldn't be ...
8
votes
3answers
412 views

Contiguous shifts in a 10-digit number

You are given a 10-digit number: 3388766112. In each move, you can select a contiguous group of digits and increase/decrease them all by the same integer, provided that each resulting digit stays ...
3
votes
1answer
58 views

Divisors ending with digits 0-9 each

What is the smallest positive integer, which has - for each of the digit 0-9 - a divisor ending with this digit?
6
votes
1answer
196 views

A 3x3 grid with common factors

A $3 \times 3$ grid $G$ is filled with every number from the set $\{2,3,5,6,7,11,14,15,30\}$. Now a new $3 \times 3$ grid $H$ is formed, such that $H_{ij}$ is the number of neighbors of $G_{ij}$ that ...
0
votes
1answer
134 views

Coloring 5 largest numbers in each row and column yields at least 25 double-colored numbers

I have a question about the answer given to this problem. The problem is reproduced below: This is a question from a very old American Mathematical Monthly, if I recall correctly. It has a very nice ...
11
votes
4answers
917 views

Deriving a 3x3 grid from another one

A $3 \times 3$ grid $G$ is filled with every number from $1$ to $9$. Now a new $3 \times 3$ grid $H$ is formed, such that $H_{ij}$ is the number of neighbors of $G_{ij}$ that are greater than $G_{ij}$....
6
votes
2answers
768 views

A square covering a rectangle

You are given a rectangle with base b and height h with $h>b>0$. What is the minimum side length of a square, which completely covers this rectangle?
3
votes
1answer
182 views

Winning strategy in game

Context: I played this game at one point (and lost) and now I'm wondering whether it was possible to win or not. We have a hexagonal board like this: I'm defining the following terms: Each hexagon ...
13
votes
1answer
407 views

Folding a piece of paper with numbers in sequence

Divide a rectangular sheet of paper with a side length of 2 × 4 into eight 1 x 1 unit squares and label them as shown in the sketch. Then fold the sheet of paper along the boundaries of the square so ...
8
votes
3answers
668 views

Perfect magic 4x4 square

Can you fill a 4x4 grid with every number from 1 to 16, such that every row, every column and every 2x2 sub-grid of numbers sum to the same value?
0
votes
1answer
75 views

Unusual 3x3 square

Can you fill a 3x3 grid with every number from 1 to 9, such that the sum of numbers in the first row is equal to the sum of numbers in every 2x2 sub-grid? Can you find multiple solutions?
0
votes
1answer
75 views

Self-indulgent numbers

Let's call a positive integer N self-indulgent of degree K>2 if for every positive integer k<K the following is true: More than half of the first k multiples N,2N,...,kN of N contain with ...
8
votes
1answer
306 views

Manual tiling with 8 dodecadudes

Here are 8 dodecadudes. (Drawn from the very numerous dodecadrafters, made from 12 half equilateral triangles, dodecadudes are a subset of 770 pieces with sharp points and narrow necks excluded). ...
8
votes
5answers
1k views

Minimize 1×3 tiles on a 5×5 table to block any more 1×3 tiles

What is the minimum number of 1×3 tiles that can be put on a 5×5 table so that no more 1×3 tiles can be put on it? Borders of a tiles are parallel to sides of the table. It is 5 but I can not prove ...
9
votes
1answer
474 views

Plants vs Zombies!

Several plants and zombies (no more than 20 creatures in total) came to the party “Plants VS Zombies”, and it turned out that all the creatures are of different heights. When a plant speaks to a lower ...
2
votes
1answer
115 views

Painting cells on the diagonals of a grid rectangle

In a grid rectangle 20210 × 1505, two diagonals are drawn, and all the cells containing segments of diagonals are painted. How many cells are painted?
0
votes
1answer
118 views

Work to time ratio! [closed]

Once Valera left the house, walked to the villa, painted 11 fence boards there, and returned home 2 hours after leaving. Another day, Valera went to the villa with Olga, together they painted 8 fence ...

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