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Questions tagged [puzzle]

This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an existing solution.

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How do we solve this disassembled rainbow bagel puzzle?

https://www.janestreet.com/puzzles/disassembled-rainbow-bagel/ I have been trying to solve this vehemently but to no avail.
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0answers
22 views

Calculating the parity of number of heads on a 8x8 chessboard?

Below is an article where I facing a problem! Please refer this completely before answering my question! Impossible Escape : http://datagenetics.com/blog/december12014/index.html I got all the sub-...
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0answers
31 views

Puzzles and exercises to improve mathematical intelligence and spatial thinking

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking?...
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28 views

Game: Removing Matches from Stacks

Given two players $A$ and $B$ and two piles of matches with size $N$ and $M$ respectively. Player $A$ goes first and players alternate turns. On each turn, the player must remove a positive number of ...
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1answer
41 views

Finding the Shortest Path passing through all Routes [closed]

I'm wondering if there's actually an easy technique (other than trial & error) to find the shortest path (which covers all paths). I googled and discovered that all paths in this diagram cannot ...
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1answer
45 views

Hard puzzle about people walking in the street. [duplicate]

We have a 1 dimensional street (straight) where people can either walk left or right. They all walk with the same speed. If two people meet they instantly change their direction (without loss of speed)...
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0answers
47 views

n coin balancing problem

Rank weights of coins with a balance scale I want to generalized above problem into $n$ coins. i.e., using balance scale, sort $n$ coins in order. Slightly more generalizing the above post, [...
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0answers
45 views

Differential equation involving brachistochrone

I have that: $$ f(x)=e^{\Psi'(x)} $$ So I took the natural log of both sides: $$ \ln(f(x))=\Psi'(x) $$ Then I integrated both sides: $$\int \ln(f(x))dx =\Psi(x).$$ Here $f(x)$ is required to be ...
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3answers
548 views

A coin flipping game

I've been thinking about the following game for a while and am curious if anyone has any ideas of how to analyze it. Problem description Say I have two biased coins: coin 1 that shows heads with ...
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0answers
102 views

The unfaithful woman that watch game of thrones without her husband [duplicate]

A city has a law that if a husband finds out one day that his wife cheats on him(by watching game of thrones without him), he must ring in the bell of the city. It is also well known to all the ...
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0answers
31 views

How to create the largest prime number using: $5,7,11$ eight times?

I can use these numbers nine times or less(repetitions are allowed), to create the largest prime number. My attempt: I know that the highest prime that could be made has to be less than $99$. The ...
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1answer
50 views

Cryptogram: $XYZ\div8 = ZX$, remainder $Y$

Say we have the division algorithm Where X,Y,Z represent a non-zero digit and the remainder is Y. What is the three-digit number XYZ? From what I gather, I re-arranged the division into an equation:...
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2answers
96 views

How to find the total number of auras possible for a tile of a given tier?

PLEASE NOTE! A different problem that uses the same ruleset (technically a subset of this one since i ask multiple questions here) that can be solved with brute force and pen-and-paper has been posted ...
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1answer
47 views

MU puzzle with an axiom it is solvable

Recently, I read about MU puzzle: https://en.wikipedia.org/wiki/MU_puzzle It is said about MU puzzle that: It can be interpreted as an analogy for a formal system — an encapsulation of ...
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0answers
13 views

Find out non-overlapping schedule to execute jobs

I have a set of 6 jobs to be run via a scheduler. Let's call them jobs A,B,C,D,E & F. 'A' & 'B' take 2 mins to complete, 'C' , 'D' , 'E' & 'F' take 3 min each to complete. No job is ...
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1answer
92 views

Expressing positive integers as $2a+4b+5c+6d$, for $a$, $b$, $c$, $d$ non-negative, with $a+c$ as small as possible

Let $n$ be a positive integer where $n > 1$ and $n \neq 3$ I need a way to return all solutions of $2a + 4b + 5c + 6d = n$ where $a, b, c$, and $d$ are non-negative integers and $a + c$ is as ...
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2answers
139 views

Prove there exists $2\times 2$ checkerboard-colored square in a $100\times 100$ table colored black and white.

"Each cell of a 100 × 100 table is painted either black or white and all the cells adjacent to the border of the table are black. It is known that in every 2 × 2 square there are cells of both colours....
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0answers
34 views

Question about a problem in Smullyan's Gödelian Puzzle Book

I'm reading the chapter "Fixed Point Puzzles" and there is a problem titled "An Open Problem" after problem #18. The chapter introduces a machine which operates on strings of upper case letters, which ...
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1answer
54 views

There are 314 coins in 21 open boxes. In each move you can take 1 coin from each of any two boxes and put them into a third box and…

There are 314 coins in 21 open boxes. In each move you can take 1 coin from each of any two boxes and put them into a third box and in the final move you take all the coins from one box. What is the ...
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3answers
60 views

puzzle on three man drinking wine

There is puzzle solution of which doesn't click for me. One person has $5$ bottles of wine, another one $3$ bottles. There is also third person. Together all three drank this $8$ bottles of wine ...
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2answers
50 views

For which $\alpha$ will take the cake ever be again with chocolate on the bottom and cream on the top

Question: A bored kid left alone at home decides to take a chocolate cream cake (chocolate on the bottom, cream on top) and his protractor and spend the day as follows: He cuts a slice of angle $\...
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0answers
82 views

Minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino.

OEIS sequence A280984 (based on this Math Stack Exchange question) describes the minimum number of dominoes on an $n \times n$ chessboard to prevent placement of another domino. The sequence ...
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1answer
124 views

Uniqueness of spanning tree on a grid.

When I was at the Graduate Student Combinatorics Conference earlier this month, someone introduced me to a puzzle game called Noodles!. The game starts with a collection of "pipes" on a grid (...
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1answer
65 views

Knights and Knaves problem from Smullyan’s “Logical Labyrinths”

I’d spent a considerable amount of time on this problem before I finally gave up and looked at the solution, where I discovered essentially the deductions identical to mine. In the solution the ...
18
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3answers
330 views

$3$ scorpions are chasing $1$ ant on the edges of a cube. The ant is $3$ times as fast than any scorpion. Can the ant survive?

The problem: Three scorpions are chasing a single ant on the edgegraph of a cube. The scorpions have the same speed ($v$), while the ant is $3$ times as fast ($3v$). They can move in any direction ...
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1answer
72 views

Two friends have $2$ natural written on their forehead. One is $2$ times the other + $1$. They can raise their hands.

The problem: Two friends have $2$ natural written on their forehead. One of them is $2$ times the other + $1$. Let's call them $X$ and $2X + 1$. They have to come up with a strategy to guess their ...
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1answer
283 views

How to determinate the the number of crossing points?

This question is an extension of the question: how-to-determine-the-convergence-the-start-and-the-finish-points. One can apply the next algoritm and obtaine the ...
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1answer
56 views

Generating all possible Domino tilings on a $4 \times 4$ grid

I have a task to write a program which generates all possible combinations of tiling domino on a $4 \times 4$ grid. I have found many articles about tilings, but it is for me quite difficult and I ...
12
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1answer
341 views

What is special about square numbers here? [duplicate]

I'm not not schooled in math. I'm 50 years old and I only have about a grade 8 level. But I do enjoy math and heard a question in the show "Growing Pains of a Teenage Genius" that interested me. So ...
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0answers
53 views

Find the heaviest ball if one weighing can be wrong.

There are 10 ball of some (can be not the same) weights, we need to find the heaviest one, but no more than one weighing can be wrong. I think that we need 19 weighings. We will weigh two balls twice ...
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2answers
63 views

Is it possible to send a suitcase with an illegal measurements inside legal one

The airport allows sending a suitcase if the sum of its length, width and height does not exceed a certain constant. Question: Is it possible to send a suitcase with an illegal measurements by ...
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0answers
67 views

Knights and knaves on a square grid

Today Gathering For Gardner posted a video by Yoshiyuki Kotani called "Liar/Truth Teller Patterns on Square Planes". The idea is that you fill a grid with knights and knaves so that both the knights ...
6
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1answer
123 views

Minimal number of questions to identify a subset

This is a curiosity question. Recently I stumbled across the following problem : Given three integers $k,m, n$ such that $m+k\leq n$. A friend chooses a subset $S\subseteq\lbrace1,\ldots,N\rbrace$...
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1answer
85 views

Finding the maximum relative misalignment of numbered rings on a combination lock?

I've been trying to figure out a general formula to calculate the maximum relative misalignment of m identical rings with n symbols each on a combination lock like the one shown below. By "maximum ...
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1answer
42 views

Generalizing this flashlight puzzle

My friend told me a riddle yesterday: four people want to cross a bridge. They each will take $1$, $2$, $5$, and $10$ minutes respectively to cross the bridge. They can go across the bridge in groups ...
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1answer
471 views

Dynamic Programming: Largest Number of Dams that can be built

Because of the recent droughts, $N$ proposals have been made to dam the Murray river. The $i$-th proposal asks to place a dam $x_i$ meters from the head of the river (i.e., from the source of the ...
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1answer
69 views

Cover a chessboard

Let $2n\times 2n $ board. I cover it with dominoes $1\times 2$ s.t. every cell is adjacent exactly one cell coverd by a domino. I have to find the maximal number of dominoes that can be placed in ...
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2answers
86 views

Is the aim of this Swap puzzle possible to achieve?

I have created the following puzzle for the Puzzling Stack Exchange and I need to know if the aim of this puzzle is possible to achieve, hence why I have firstly posted it here. I hope it is not off-...
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0answers
68 views

What is the probability of being the last to touch an object passed around a circle of $N+1$ people?

We have $n+ 1$ people numbered by $0,1,...,n$ standing in a circle. Person $0$ has a bag of chips to start passing around. Every time, the person $k$ who is holding the bag of chips has probability $...
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1answer
63 views

“Human Knot” solvability probability

Somewhat surprisingly, I don't see a question about this. There is a team-building (or just fun mathematical) game where a group of people hold hands with each other, usually trying not to hold hands ...
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0answers
58 views

Catching the mole problem best winning strategy

The problem is: There is a mole and n holes named with numbers $1, 2, 3, \ldots, n-1, n$. The mole can start from any hole and each day it can move only from a hole to a consecutive hole. So if the ...
4
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2answers
119 views

Let consider a square $10$x$10$ and write in the every unit square the numbers from $1$ to $100$

Let consider a square $10\times 10$ and write in the every unit square the numbers from $1$ to $100$ such that every two consecutive numbers are in squares ...
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1answer
75 views

Generalizing tug-of-war puzzle

A puzzle at the end of a 3Blue1Brown video asks the following question (paraphrased): From a group of 20 people, you get to send one person to participate in a tug-of-war tournament. You don't care ...
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2answers
77 views

Dudeney’s solutions to haberdasher's problem exact measures of sections

What is the IG length if the side of the square is 1? I wonder if it is half of the square side. The triangle below represents the haberdasher's problem. version 2 version 1 (added after edit, here ...
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1answer
32 views

Estimating worth of coins by weight.

I was given this riddle that has been bothering my mind for past few hours. Given the following information: the weight of coin types: 1p - 1.62g 2p - 2.11g 5p - 2.57g 10p - 2.49g 20p - 3....
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2answers
93 views

Number of different fault-free $2 \times 1$ domino tilings on a $6 \times 5$ rectangle

Fifteen $2 \times 1$ dominoes can be used to tile a $6 \times 5$ rectangle. In tiling the rectangle we might generate what are known as fault-lines. A fault-line is any horizontal or vertical line ...
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1answer
64 views

Can somebody elaborate the maths behind this problem?

Theatre Square in the capital city of Berland has a rectangular shape with the size n × m meters. On the occasion of the city's anniversary, a decision was taken to pave the Square with square granite ...
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0answers
62 views

Maths riddle- clocks

The clock in the maths department common room is faulty. At twenty past three on Wednesday afternoon it shows 11.25. The clock in fact goes a bit slow and backwards, covering 55 minutes in every hour. ...
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3answers
42 views

M is nice if it is possible to make it all + by a set of operation, each consisting of changing the sign of one row or the sign of one column.

Let $M$ be an $n\times n$ matrix whose entries are $+$ and $-$. Call $M$ nice if it is possible to make it all $+$ by a set of operation, each consisting of changing the sign of one row or the sign ...
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1answer
35 views

Finding similarities between binary strings

I have been tasked with this puzzle for my programming class, it's purely a puzzle and doesn't count towards any grades, but not being able to solve it is really bugging me! We have been given two ...