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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.

4
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1answer
93 views
+100

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 (...
-2
votes
0answers
21 views

“Align” ring squares to a uniform color

A ring of N squares, the N is a multiple of 3. "K" squares in the ring are painted of white, and the other squares are painted black. We have a SWITCH operator, that turns the color of 3 adjacent ...
4
votes
1answer
1k views

Calculating Total Amount of Money Based on Weight

Dealing with US Dollars... Assuming we know the weights of half-dollars, quarters, dimes, nickels, and pennies. Also assuming the weights remain constant (don't change from one quarter to another ...
6
votes
2answers
293 views

Rosenfeld's $7 \times 7$ square puzzle

A $7 \times 7$ square puzzle may be described as following. Start with a $7 \times 7$ square divided into $7 \cdot 7$ unit squares. First select a unit square and mark it. And then, in each ...
3
votes
0answers
43 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 ...
1
vote
1answer
44 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 ...
6
votes
1answer
77 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 ...
4
votes
0answers
63 views

$3$ scorpions are chasing $1$ ant on the edges of a cube. The ant is $3$ times faster 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 faster ($3v$). They can move in any direction and ...
5
votes
1answer
64 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 ...
1
vote
1answer
47 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
332 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
1answer
483 views

Word Problem Proof? (just for fun, help)

Players $1, 2, 3,\dots, n$ are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player ...
1
vote
0answers
45 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
53 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 ...
6
votes
1answer
114 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 $S\subseteq\lbrace1,\ldots,N\rbrace$...
1
vote
1answer
55 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 ...
0
votes
1answer
371 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 ...
5
votes
0answers
54 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 ...
8
votes
1answer
239 views

Removing points from a triangular array without losing information

I'm trying to find insights about the following puzzle, to see if I can find it on the OEIS (and add it if it's not already there): Suppose I give you a triangular array of light bulbs with side ...
0
votes
1answer
57 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 ...
0
votes
1answer
32 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 ...
4
votes
2answers
117 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 ...
1
vote
2answers
55 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-...
3
votes
2answers
61 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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0answers
25 views

Find the number of the house [duplicate]

A certain street has between 50 and 500 houses in a row, numbered 1, 2, 3, 4, … consecutively. There is a certain house on the street such that the sum of all the house numbers to the left side of it ...
2
votes
0answers
63 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 $...
0
votes
1answer
23 views

General solution to water jug problem with limited amount of water

The Problem goes as follows: There are 3 water containers of different sizes: 10 liters, 7 liters, and 3 liters. If we start by having 10 liters of water in the 10 liters container, and There is ...
5
votes
2answers
307 views

Colored graph with $2$ colors

Let us call $G$ a graph with vertices in two possible colours. If we select a vertex, we change the colour of it and of every vertex that is adjacent to it. Is it possible to change a graph from all ...
5
votes
1answer
114 views

Proof that $n$ planes cut a solid torus into a maximum of $\frac16(n^3+3n^2+8n)$ pieces

Question: How many pieces can a solid torus be cut into with three (affine) planar cuts? A google search will quickly reveal that the answer is thirteen, as can be read about here. The picture below ...
3
votes
0answers
57 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 ...
2
votes
1answer
61 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 ...
15
votes
1answer
289 views

Is $k^{2018}+2018$ prime for some positive integer $k$ ? If yes, which $k$ is the smallest?

Is there a positive integer $k$, such that $k^{2018}+2018$ is prime ? If yes, which $k$ is the smallest ? According to my calculation, $k$ must be greater than $10^5$ and therefore such a prime must ...
0
votes
1answer
51 views

Optimal moves for maximizing perimeter? [closed]

Herman and Alex play a game on a $5 \times 5$ board. On his turn, a player can claim any open square as his territory. Once all the squares are claimed, the winner is the player whose territory has ...
2
votes
2answers
70 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 ...
0
votes
1answer
29 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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votes
1answer
60 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 ...
0
votes
0answers
55 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. ...
0
votes
3answers
40 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 ...
0
votes
3answers
78 views

Math puzzles suitable for printing on a mug

I need to design a cup for a reception for first-year college students and i'm searching for some challenging and entertaining math puzzle or game to use. Previous years it has been used the "Three ...
0
votes
1answer
61 views

Non self-referential statement in answering truth-liers puzzles.

As it goes, there are knights, who always tell the truth, and knaves, who always right. Suppose, a question is that there are a knight and a knave, and we have to find out if a Statement S is true or ...
1
vote
1answer
32 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 ...
2
votes
3answers
37 views

If $85_b = 58_c$, what is the smallest possible value of $b$?

I have searched and watched videos online and can't find a method to solve this problem: If $85_b=58_c$ for some positive integer bases $b$ and $c$, what is the smallest possible value for $b$?
9
votes
5answers
5k views

Variation on the Monty Hall Problem

Many of us know the Monty Hall Problem But the other day I was asked a variation of this riddle. The answer of the original question is, of course, $ 66\% $ in favor of changing doors, but this is ...
0
votes
2answers
4k views

Faulty machine problem variation

I don't know if this problem is known by any other name. The classic problem is: We have 10 machines that produce balls, each weighing 10grams. One of the machines, however, produces balls weighing 9 ...
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0answers
24 views

Probability boxes (precious vs ordinary stones)

We play in a television game. We have 8 identical and indistinguishable boxes, each of which has 2 pebbles. Any pebble can be precious or not. We pick a box and the host, without looking at it, pulls ...
0
votes
2answers
853 views

Fifty minutes ago if it was four times as many minutes past three o'clock. How many minutes is it to six o'clock?

Fifty minutes ago if it was four times as many minutes past three o'clock. How many minutes is it to six o'clock? According to the question the present time is in between 3 o' clock and 6 o' clock. ...
5
votes
1answer
158 views

Alice and Bob take turns to remove numbers from a list

Alice and Bob play the following game. In the beginning there is list of numbers $$\{0, 1, 2,\dotsc, 1024\}.$$ Alice starts, and removes 512 numbers of her choice. Bob continues and removes 256 ...
0
votes
1answer
45 views

Does this question provide enough information to answer?

Lewis Carroll posed the following problem: Two travelers spent from 2 o’clock until 9 walking along a level road up a hill and home again; their pace on the level being $x$ miles per hour, uphill $...
1
vote
3answers
52 views

rock scissor paper probability

Alice and Bob played 25 games of rock-paper-scissors. Alice played rock 12 times, scissors 6 times, and paper 7 times. Bob played rock 13 times, scissors 9 times, and paper 3 times. If there were no ...
0
votes
1answer
59 views

Guess ball colors

7 people receive either a black or a white ball. They can only see the color of the others balls, but not their own. Both of the colors are equally likely. They play as a team a game of guessing their ...