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.

2
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1answer
43 views

Hat guessing with 100 hats case

My question is regarding to the question which was asked here: A riddle about guessing hat colours (which is not among the commonly known ones) $100$ prisoners are put a hat on top of their head, ...
0
votes
2answers
56 views

Find the shaded part area?

Two squares of side 5 and 2 respectively. They are touching each other. Diagonals of the square are joined. find the area of the shaded part?
4
votes
0answers
63 views

$100$ prisoners problem - But here they write their guess on paper [duplicate]

A variant of the $100$ prisoners problem. $100$ prisoners are given each either a white hat or a black hat. They can see each other's hat but not their own and they cannot communicate. Each ...
1
vote
0answers
53 views

Four frogs are located at the corners of a square on the plane [duplicate]

Four frogs are located at the corners of a square on the plane. At each step a frog jumps over another frog and lands in the symmetrically opposite location. Question: Can the frogs find a way to ...
0
votes
1answer
53 views

how many guards are needed to protect a king from an assassin in n-torus ($\mathbb R^n/\mathbb Z^n$) [closed]

Question: how many guards are needed to protect a king from an assassin if all of them are located on the $n$-torus $\mathbb R^n/\mathbb Z^n$? The location of the king and the assassin are known, ...
0
votes
2answers
60 views

Solving the recurrence $g(n)=g(n-1)\left(1+\frac{1}{n}\right)+\left(1+\frac{1}{n}\right)$ with $g(0)=0$

I ran across the following math puzzle: a mouse is on a circle with circumference of 100 units and every turn he walks on the circle a unit of 1 after every turn the circle is increased by 100 units (...
4
votes
2answers
79 views

Proving all variables are equal

I came across a puzzle lately. Let $A$ be a matrix of size $(2n+1)$ by $(2n+1)$. The diagonal of $A$ is all zeros. Every other entry of $A$ is either $+1$ or $-1$. Each row of $A$ sum to zero. In ...
21
votes
3answers
350 views

Black and white shirts puzzle

I’m not familiar enough with probability to be able to even begin to approach this myself, but this puzzle has been plaguing me. Assume I have $m$ black shirts and $n$ white shirts, where $m > n$. ...
1
vote
1answer
88 views

Partition of a rectangle into squares problem

recently I encountered this problem: "Show that a rectangle can be partitioned into finitely many squares if and only if the ratio of its sides is rational." I have found the a solution which I need ...
5
votes
4answers
192 views

Solve Riddle With Algebra

There is a riddle and I believe it can be solved by algebra - please assist A boy has as many sisters as brothers, but each sister has only half as many sisters as brothers. How many brothers and ...
1
vote
1answer
68 views

Explanation of Freeman Dyson's solution of the counterfeit coin problem

Freeman Dyson's paper, The problem of the pennies Math. Gaz., 30 (1946) 231-234, offers a solution to a counterfeit coin detection problem. I quote his solution of one case as follows. I would ...
1
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0answers
51 views

5x5 Bingo Puzzle (odds)

I have a question that is very similar to this one 5x5 Bingo Puzzle [Logical thinking problem]. 5 people participate in a custom game. They are given blank cards, in which they have to fill numbers ...
0
votes
2answers
81 views

Searching for a special book in the Library of Babel

In The Library of Babel, there are all the possible 410-page books of a certain format and character set. There is a legendary book, called a total book, which is supposed to be the catalogue of the ...
8
votes
4answers
656 views

Is there a general effective method to solve Smullyan style Knights and Knaves problems? Is the truth table method the most appropriate one?

Below, an attempt at solving a knight/knave puzzle using the truth table method. Are there other methods? Source : https://en.wikipedia.org/wiki/Knights_and_Knaves
0
votes
1answer
25 views

Total number of ways to arrange objects subject to constraint [duplicate]

Suppose that you are ticket collector in Cinema office. It cost 50 dollars to watch a movie. There are 20 people in line. 10 people in that line have exactly 100 dollar bills and 10 people have ...
0
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0answers
35 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-...
0
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0answers
39 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?...
0
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0answers
33 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 ...
-1
votes
1answer
43 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 ...
0
votes
1answer
56 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)...
1
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0answers
54 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, [...
1
vote
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 ...
31
votes
3answers
637 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 ...
0
votes
0answers
34 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 ...
3
votes
1answer
53 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:...
1
vote
2answers
104 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 ...
0
votes
1answer
49 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 ...
0
votes
0answers
16 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 ...
0
votes
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 ...
7
votes
2answers
148 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....
0
votes
0answers
36 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 ...
0
votes
1answer
56 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 ...
1
vote
3answers
64 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 ...
3
votes
2answers
52 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 $\...
4
votes
0answers
123 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 ...
8
votes
1answer
129 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 (...
1
vote
1answer
70 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
votes
3answers
366 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 ...
5
votes
1answer
73 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 ...
4
votes
1answer
300 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 ...
1
vote
1answer
57 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
votes
1answer
343 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 ...
1
vote
0answers
55 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 ...
2
votes
2answers
65 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 ...
5
votes
0answers
70 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
votes
1answer
125 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 $S\subseteq\lbrace1,\ldots,N\rbrace$...
6
votes
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 ...
0
votes
1answer
43 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 ...
0
votes
1answer
480 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 ...
1
vote
1answer
70 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 ...