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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 ...

2
votes
2answers
77 views

To Mock a Mockingbird: The Barber of Seville 3 (logic puzzle)

This is the "Barber for a Day" problem from Raymond Smullyan's To Mock a Mockingbird. A certain town contained exactly 365 male inhabitants. During one year, which was not a leap year, it was ...
0
votes
1answer
34 views

The election of knights and knaves [on hold]

One year, $n$ (three or more) candidates came out in the election to select the mayor of the island of knights and knaves. In one TV debate, all the candidates stated in turn: For each $k = 1, 2, 3, \...
6
votes
1answer
121 views

Mathematical guessing

A total of 2,879 votes have been distributed among the seven candidates in a one-party primary election. It is known that none of the candidates has obtained the same number of votes as another and ...
0
votes
2answers
67 views

Puzzle relation with geomtry

An army $40$ km long is moving at constant speed. A horseman takes a message from the rear end of the army to the general in the front end of the army and returns back to the rear end of the army (...
-3
votes
0answers
55 views

Interesting and hard question for me. [on hold]

I showed that an interesting question. I don't know answers. The borders of our world in any part of a country the bell is ringing. When the bell rings the number of unknown airports airplane take ...
0
votes
0answers
21 views

How many latin-square designs are orthogonal to this 4x4 latin square design

Where this Latin Square is similar to sudoku, in which each row has one and only one of 1,2,3 and 4, and each column has one and only one 1,2,3 and 4. Important: orthogonality means that the new ...
2
votes
3answers
46 views

Changing my Clock

I was given a problem in class. Let's say I bought a clock with no numbers on it (has only the hands). Because of the recent time change, I had to change my clock one hour back. In order to do this, I ...
1
vote
0answers
42 views

Godelian problems with logic puzzles

It occurs to me that the sort of reasoning common in many logic puzzles (e.g. https://en.wikipedia.org/wiki/Hat_puzzle or https://xkcd.com/blue_eyes.html), the persons involved all trust one another ...
0
votes
1answer
29 views

Prettiest princess puzzle - probabilisticly finding maximum in a finite set with one scan

I've encountered a mathematical puzzle with an enlightening solution - sadly I recall only the outline of the solution without the specifics. The puzzle went somewhat as follows: A king with many ...
0
votes
1answer
53 views

Show that the first child can not win

Three children have 10 pieces numbered from 0 to 9 on both sides. They play the following game: -The first child chooses a piece, so a number, preserves it and passes the number on a sheet -The ...
2
votes
1answer
50 views

What would be the chances of solving a standart 3000 piece puzzle completely at random?

I LOVE puzzeling, but this one question always bothered me. And for that I am not good at maths, I couldn't really work it out. Here is the problem: Say I have a 3000 pieces puzzle and I blindfold ...
0
votes
0answers
54 views

The black/white hat problem. Is it 50-50?

I was asking my friends a riddle about identifying hats. Each person has to correctly identify the colour of their own hat that was put on their head randomlly. There is no defined number of either ...
5
votes
3answers
83 views

How many ways to place three distinguishable tokens on the white spaces of a $4$-by-$4$ chess board?

Consider a $4\times 4$ chessboard like the one showing above. You want to place 3 distinguishable tokens. Each piece can only be placed in a white square, with only one piece per row and per column. ...
1
vote
1answer
27 views

Ways to uniquely specify a line in the plane

The following puzzle occurred to me: Suppose we want to devise a code such that given any line in the plane, you can give me $k$ real numbers, and from this information I can uniquely determine the ...
2
votes
1answer
29 views

What is generated by $(1265)$, $(2376)$, and $(3487)$? (Pocket cube group)

I am trying to find the group structure $G$ of the $2\times 2\times 2$ Rubik's cube, or the "pocket cube," and I have determined that it is isomorphic to the group of permutations on $8$ numbers ...
4
votes
2answers
253 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 ...
8
votes
2answers
94 views

Group structure of rotating-square puzzle

Suppose we arrange the numbers $1$ through $6$ at the "vertices" of the shape formed by aligning the sides of two squares, as shown below: In this "puzzle," the only moves allowed are rotating the ...
1
vote
1answer
86 views

What is the minimum amount of moves it takes to finish this game?

This is a follow up question from this post which I asked. The previous question was answered by Barry Cipra, and I was suggested to create this follow up question. The Game: Two players have $...
-1
votes
2answers
47 views

How much refund is due? tricky one!

A person moves into a property on 9th Sep 2015 for a rent of £1300 per month. He pays money on 9th of each month. he vacates property on 5th of September 2018. As he had paid £1300 on 9th August 2018, ...
0
votes
1answer
40 views

How to solve this Yes/No query problem where we need to find the number of sets satisfying the given condition?

So let's say we have 2 people playing a game. Let the first person be $A$ and the second person be $B$. So $A$ guesses a number between $1$ and $n$ ( say $x$) and $B$ gives queries to $A$ in form of $(...
1
vote
1answer
35 views
1
vote
0answers
28 views

Classifying Customers by Purchase Periodicity

I want to classify retail customers into groups reflecting the periodicity of their purchasing behaviors: e.g. weekly, monthly, seasonal, annual, etc. I thought this question was trivial, but now find ...
2
votes
2answers
67 views

Lower Bound on God's Number in the Rubik's Cube

I'm trying to write a project about the Rubik's Cube, and althought it's easy to find out the lower bound (using half turns) is 18, finding a precise proof hereof seems impossible. How does one proof ...
2
votes
0answers
30 views

Polynomials with equal minima and maxima

I wonder how to construct a polyomial $P(x)$ of even degree $N$ with $n = \frac{N}{2}$ equal minima $x_i$, i.e. $P(x_i) = \text{m}$ for all $x_i$ $n -1$ equal maxima $X_i$, i.e. $P(X_i) = \text{M}$ ...
2
votes
0answers
52 views

Characterization of polynomials by their “shape”

Let me show how a general "shape" of a polynomial $P(x)$ of degree $n$ can be uniquely characterized by a sequence of small integers of length at most $n-3$. Let $\{ e_1,\dots,e_m \}$ be the extrema ...
0
votes
0answers
11 views

Select the suitable figure from the four alternatives that would complete the square matrix.

Tried to find different clues from the image such as counting sides, shapes, sizes etc. but no solid clue found. I think the answer is 'D', requesting your opinions.
1
vote
2answers
37 views

Whose hat was taken by P, how and why?

Four brothers go to a dance party. As the leave,each of the brother accidentally takes a hat belonging to another brother and the coat belonging to the third brother. M takes the court belonging to ...
2
votes
0answers
66 views

A Logic Puzzle: Explanation Of The Solution

I am trying to understand the solution to a logic puzzle, but it confuses me on many levels The problem is this: And the solution is this: What confuses me is the following: Why would it ...
0
votes
0answers
18 views

Is 3 bits difference enough to map distinct values toggling a single bit in a binary number?

Assume that one can only alter a single bit in a binary number set. As in: 00000000 can be converted to one of the rows in: ...
1
vote
1answer
31 views

Seating arrangement problem, 16 guests, 4 tables, 5 courses

I am organizing a dinner for 16 guests in a dining room with 4 tables of 4 seats. There are 5 courses in which the guests may change seats. Is it possible to devise a seating arrangement such that ...
0
votes
1answer
106 views

A math riddle involving sums of digits

When I was in highschool I became obsessed with this strange combination I discovered. I don't really know a lot about math but I've recently re-discovered it and believe I have found an answer, but ...
0
votes
1answer
38 views

What is the logic behind this puzzle's answer?

Keep a number between $1$ and $60$, including $1$ and $60$. The aim is to find kept the number. $1,3,5,7,9,\\ 11,13,15,17,19,\\ 21,23,25,27,29,\\ 31,33,35,37,39,\\ 41,43,45,47,49,\\ 51,53,55,57,59\...
5
votes
1answer
58 views

Riddle of the fox and the holes, with n holes

I was wondering if the problem of fox and holes (There are five holes in a line. One of them is occupied by a fox. Each night, the fox moves to a neighboring hole, either to the left or to the ...
1
vote
4answers
46 views

$42$ (U.S.) coins make $\$1$. If there's at least one quarter, dime, nickel, and penny, find the number of dimes and nickels.

My piggy bank has $42$ coins worth exactly $\$1.00$. If it has at least one quarter, dime, nickel, and penny, find the total number of dimes and nickels. I found $1+ 5 + 10 +25 =41$ cents with the ...
0
votes
1answer
43 views

Points table in a tournament

There are $7$ teams in a tournament. Each team plays exactly one match against every other team. (Total of $21$ matches). Teams get $2$ points for a win, $1$ point for a draw and $0$ points for a loss....
-1
votes
1answer
32 views

Article Price: A Methodical Approach

From Mathematics For Pleasure Paperback by Oswald Jacoby and William H. Benson (1965) A certain article costs an amount which requires a minimum of four standard United States coins to pay for it....
-1
votes
2answers
51 views

How did we know that X must be equal to 1? [closed]

I did not understand the solution to this problem
10
votes
2answers
586 views

Armed with a sword and a shield, a proud knight combats a monstrous hydra with 100 heads.

Hi so I am battling with this question at the moment. "Armed with a sword and a shield, a proud knight combats a monstrous hydra with 100 heads. When he slashes, he removes 17 heads and 5 heads grow ...
0
votes
4answers
71 views

Find the unknown area by different methods

this problem has many ways of calculating, could provide some solutions, particularly using proportions EDIT : A it's not midpoint
0
votes
4answers
60 views

Filling pool with 3 hoses puzzle!

I'm stumped on a math puzzle and I can't find an answer to it anywhere! A man is filling a pool from 3 hoses. Hose A could fill it in 2 hours, hose B could fill it in 3 hours and hose C can fill it in ...
1
vote
4answers
133 views

What is the probability that Fra wins?

Fra and Sam want to play a game. They have two classic coins Head-Tail. They flip the coins at the same time. If the result is $HH$, Fra wins. If the result is $HT$ (or $TH$), they flip again and ...
0
votes
0answers
43 views

Hat-guessing problem for finitely many prisoners and infinite sets of hat colors and the Axiom of Choice

In the "easy" version of the hat-guessing problem, there are n prisoners (say, 100) facing forward in a line, wearing hats with colors from a set $H$ in a sequence decided by the warden. Each can only ...
2
votes
4answers
191 views

The problem of dividing 3kg flour to three 1kg parts using a balance

Suppose you have 3kg flour, and you are asked to divide it to three 1kg parts using a balance scale. It seems to me that it's impossible to do with a finite number of weighing, but I can't see how ...
0
votes
0answers
15 views

I alphabetize a large number of two-letter words. What is the expected ratio of words starting with A to words starting with B?

I store my journal papers in a folder, ordered alphabetically by the name of the first author. Assume that each paper has two authors, ordered alphabetically. Assume also that each author name is ...
1
vote
1answer
114 views

The 3 Gods riddle

I'm not entirely sure which boards would be the correct one for this, however as this board does answer logical question I posted here. https://en.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever In ...
2
votes
1answer
126 views

How does the three piles magic trick work?

When I was growing up, my parents taught me a simple magic trick that consisted in making three piles of cards and guessing my card, even when they hadn't even touched the deck. The trick in itself ...
-2
votes
1answer
72 views

find the treasure.

Guys I just started college ( engineering) so if this question was easy just help me out please. There are three boxes,and three messages: Message 1 / box 1: the treasure is not in the box 1. ...
1
vote
2answers
57 views

Given a painted cube composed of smaller cubes, what is the probability of an unpainted cube given you see 5 unpainted faces? [closed]

For a cube composed of $3 \times 3 \times 3$ smaller cubes has the outside painted red. If a small cube is placed on the table and you see all $5$ visible faces are unpainted, what is the probability ...
1
vote
1answer
73 views

What's the formula for the number of possible answers to this puzzle?

I'm trying to find what the formula is for the number of possible variations to this puzzle. I know that there is only one answer (or 4, when taking into account the variations when the grid is ...