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
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1answer
35 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
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1answer
115 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 ...
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2answers
140 views

How much water can Rickey Rat carry up the stairs in leaky buckets? [closed]

A powerful sorcerer has hired Rickey Rat as an intern. The wizard gives Rick the task of carrying water from a well to the garden. The path from the well to the garden is up a staircase with 1000 ...
3
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3answers
213 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
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1answer
106 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 ...
8
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1answer
786 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 ...
5
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5answers
303 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 ...
10
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3answers
319 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 ...
7
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3answers
406 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
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1answer
56 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?
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0answers
72 views

Make numbers 1-100 using the digits 2, 0, 2, 2 [closed]

Rules: Must use all numbers 2, 0, 2, 2 combined to form an equation that equals 1-100 The order of 2, 0, 2, 2 can be reversed Except for 2, 0, 2, 2, no other numbers can be used You can use 2, 0, 2, ...
6
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1answer
194 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
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1answer
133 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
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4answers
912 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
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2answers
765 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
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1answer
179 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
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1answer
403 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
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3answers
665 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
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1answer
72 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
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1answer
73 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 ...
-3
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0answers
76 views

MATHEMATICAL HARD SEQUENCE [closed]

13, 20, 7, 5033, 22, 20, 2, 0, 23, 115, 17, ? This sequence seems impossible to solve because it might even contain two or more parallel sequences. I would appreciate any help.
8
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1answer
301 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
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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
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1answer
471 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
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1answer
113 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
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1answer
117 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 ...
7
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5answers
1k views

Split 1 through 6 into a product of 24 and sum of 12

How many ways are there to split the numbers 1, 2, 3, 4, 5, and 6 into two groups, such that the product of the numbers in one group is 24 and the sum of the numbers in the other group is 12? An ...
12
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1answer
382 views

Strange tiling pattern

Here is a simple pentagonal shape: Using copies of this shape it seems that you can tile the plane, without even needing to flip over the tile. But can you really?
3
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2answers
412 views

Find X and Y so that they are never equal [closed]

In a game, your opponent is given an ordered pair of integers (X, Y), and at each step, they can either double X and add one to Y or double Y and add one to X. Here's an example sequence of steps that ...
9
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2answers
429 views

Construction of positive integers by given rules

For a positive integer n there are two operations defined: append one of the digits 0, 4 or 8 at the right end of n n can be divided by 2 if n is even Start number is 4. Is it possible to construct ...
3
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1answer
180 views

Infinite beauty

This is a follow-up to Puzzle about 6 infinite cylinders in space Question: Given six identical infinite (no caps) cylinders is there a beautiful arrangement in space such that each touches each ...
2
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2answers
337 views

Traffic light controller

Consider the following diagram. Once every 2 seconds a car enters from the top and travels down towards the exit. Once every 3 seconds a car enters from the left and travels to the right exit. In the ...
3
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2answers
498 views

Cubes touching all other cubes

This question is based on this great puzzle: Puzzle about 6 infinite cylinders in space What is the most number of identical cubes that can be placed, such that every cube touches all the other cubes ...
3
votes
1answer
148 views

9 people sitting at a round table

I am unable to figure out how to solve this question @Joffan has given an answer but he hasn't mentioned much regarding his approach. I requested him but he still didn't give a clear answer. This is ...
4
votes
2answers
419 views

A geometric puzzle. What is the angle?

This is a simply stated geometry puzzle. What is the angle p in this isosceles triangle? Here's some information about the origin of the puzzle. Following any links therein may spoil the fun if you ...
13
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2answers
1k views

Puzzle about 6 infinite cylinders in space

You have 6 infinitely long cylinders (tubes) with the same radius R. Can you arrange them in space in a way that every cylinder touches the other 5? By touching, I mean have a common point or a line. ...
3
votes
2answers
245 views

Country Outliers

You are given a note from a language nerd, which is: If Japan is 239, Then Germany is 4. Greece is 14, While Italy is 3. Now, Philippines has 412. But Norway has 2357! Now you are given 3 questions: ...
2
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1answer
108 views

Patterns - they're everywhere!

You wake up in a room (again) that has two floors, Both have 3 puzzles. In order to escape, You have to find every answer in this order: Red Yellow Green Cyan Navy Pink and combine it together (eg if ...
8
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5answers
1k views

A pentagon puzzle

Consider the following pattern made of regular pentagons: If the pattern continued, will it form a complete loop or will the pentagons overlap?
12
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3answers
715 views

Outmaneuver your opponents in the duel

A, B and C are in a three way duel. Starting with A, they rotate in the order of A-B-C, each firing one shot at a time. They stand close to one another, so that each can kill one of the others or ...
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2answers
106 views

Surrounding an equilateral triangle

You are given an equilateral triangle. What is the most number of such identical triangles you can place such that they do not overlap, but each one touches the original triangle?
3
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2answers
323 views

Pumping triangles

On the inside of the triangle (0,0),(1,0),(0,1), define the "pretty useless map" or pump by the following prescription: Given a point A find its projections x0,y0 to the x and y axes and ...
1
vote
0answers
74 views

What's the rule? [closed]

Given the list of ordered pairs: (1,1), (2,2), (3,3), (4,4), (5,5), (1,4), (2,4), (1,2), (3,1), (5,1), (3,5) 1 and 2 make 4 laugh, but only 5 makes 1 laugh. What's the rule? I've been staring at ...
11
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1answer
287 views

Don't Pair Program a Puzzle

My friend William and I wanted to make a word search (number search?) of five digit numbers in a 5x5 grid, filling all spaces to form 12 clues. To simplify things, we decided we would add a single ...
10
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2answers
582 views

Two football teams

Twenty two football players have agreed to split every week into two teams and play a match against each other. Every week, teams will be chosen differently, 11 players in each team, and they will ...
0
votes
1answer
133 views

What is the next diagram, and what is the number?

I needed some help to a friend of mine, he was solving a puzzle. He sent me a remake of what he was solving, and its up to you to help my friend! Note: My friend says that he messed up at 32, there ...
8
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6answers
2k views

5 points on a ball, divide the ball into 2 halves so that one half as exactly 4 points

Suppose that you take a pen and mark five points on a ball. I claim that no matter where you draw those points, I can always slice the ball into two equal halves (two equal and closed hemispheres) ...
0
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1answer
81 views

Not a music rebus

What is the 6-letter word that associates with this rebus? Helpness Meter 1: Helpness Meter 2:
0
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1answer
85 views

Trail passing through squares of a grid

Let's construct a 10x10 grid. 0n the 100 squares you are allowed to place 7 bases (the red dots in the diagram below) in any square on the grid. Then you fill the grid with skinny trominoes. The ...
0
votes
1answer
55 views

Largest 5-digit palindrome in base 16, where each digit appears at most twice

What is the largest number $ x $ such that $ x_{16}, $ i.e. $ x $ in base 16, is a 5-digit long palindrome, where each digit appears at most twice? A palindrome is a number that reads the same forward ...

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