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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 ...

1
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1answer
90 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
60 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 ...
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votes
1answer
67 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
49 views

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

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
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1answer
60 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 ...
7
votes
1answer
68 views

16-puzzle: confusion over the number of inversions

For one of my homework questions we were given a 16-puzzle and we had to find out if it is solvable; and then solve it. My 16-puzzle is \begin{array}{|c|c|c|c|}\hline 1&2&3&4\\\hline 5&...
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votes
2answers
22 views

Addition with ones and tens [closed]

The children on the planet Veeton count in Zips and Zaps. If the sum is correct how many Zaps make a Zip? \begin{array}{ccc} & \text{Zips} & \text{Zaps} \\ & 3 & 8 ...
0
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1answer
33 views

Number of measures in music

I am interested in calculating the number of possible measures. (as used in music, synonymously: bar) Given is the number of beats per measure (e. g. 4/4 = measure length 1) and a set of possible ...
6
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0answers
86 views

Impossible permutations of the Gear Cube

If you're familiar with the group properties of the Rubik's Cube, you will probably know that, under the action of the standard moves, all possible permutations of the (unoriented) edge pieces are ...
3
votes
1answer
61 views

(Puzzle) Find the area of the orange quadrilateral in the given figure

Given: in the figure below, ABCD is a square, and DH=CG=FB=AE. Areas of quadrilaterals green, red and blue are given in the figure. Find: area of the orange quadrilateral. I'm struggling with ...
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votes
1answer
58 views

cracking a word code [closed]

edited my word code -- Of course everyone may boo this problem saying its not math enough and more of a 'riddle me this' type question. But I think it's math very much so as I got as far as to ...
1
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0answers
55 views

How long message can I send?

I know the $n$-bit message ($M$). I have to send it to the receiver bit by bit. For each bit I can also send one bit of comment ($C$). Before receiver gets the bit, he have to guess it($G$). After ...
5
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3answers
228 views

If $A=1$, $B=2$, etc, then what word, treated as a product of its letters, has value closest to $1000000$?

Suppose that a product $n$ is the product of the numbers corresponding to its letter, eg. $A = 1$, $B = 2$, etc. What is the word that has a product close $1000000$? Here's some examples: $$\begin{...
13
votes
1answer
405 views

Finding a combinatorial formula for the following sequence of tables

While studying a subject in mathematical physics and topology (which is not necessarily relevant to this question anyway), I bumped into the following sequence of tables, let's call them $M_0, M_1, ...
1
vote
1answer
43 views

What recommendations can be used to speed up solving a logic puzzle problem involving placing in order a set of elements using a logic grid?

The problem is as follows: A group of archaeologists found an artifact to which they believe tells an account of the results of a race in an ancient Hippodrome. After days of studying the ...
1
vote
1answer
37 views

Find area of square in circle (puzzle)

Source of question : https://nrich.maths.org/548 Question=Find area of the shaded/inscribed part of the shape. I have got the answer for the first two shaded shapes , however the I cannot find a way ...
1
vote
4answers
60 views

Problems About Logic: Alice, Bob, and Charlie, who is the one that telling lie?

I have problem to solve, Three people have their own statement: Alice : If Bob tells lie, then Charlie tells lie too Bob : If Charlie tells lie, then Alice tells lie too Charlie : If Alice tells ...
19
votes
3answers
674 views

What is the relationship between 1/7, 1/11, 1/13, and the number 1001?

Here is what we have: 1/7 = 0.142857... 1/11 = 0.090909... 1/13 = 0.076923... Notice that if you add the first three digits to the next three digits, you always ...
2
votes
1answer
102 views

Max product for a list of digits

There is a list of digits, lets say: "1", "1", "9", "9" And a multiply operator; how to make the max product. The answer for above example is: ...
0
votes
0answers
53 views

Help with a puzzle from an old book

I found a very nice puzzle from a old book written in Spanish. I got stuck after a few hours, the only possible solution I found was that the numbers inside the circle have a kind of succession. For ...
0
votes
0answers
12 views

What is a seriation problem given a similarity matrix?

I am told that given a similarity matrix between objects, the seriation problem can be solved by permutting the rows and columns of the matrix such that larger values congregate in the main diagonal ...
1
vote
1answer
34 views

Dice game keep rolling [closed]

There is a dice game where both players roll a fair dice once. If player A rolls a 1, then he keeps rolling. And in the end, if the score is tied, player B wins. What is the probability of player A ...
2
votes
0answers
58 views

Is there an easier (or alternative) method to uncover the answer, as opposed to brute-force/exhaustion?

Here is a puzzle I made (I originally posted it here on the Puzzling Stack Exchange): Suppose you constructed $m$ rows in the following way ($m,n$ are integers): $$\begin{align}&1,2,3,\ldots ,n ...
1
vote
1answer
51 views

Possibilty of a number $n$ to be a multiple of $x$ that has a remainder of $y$

Is there a formula or solution for this : "$n$ is a number that is a multiple of $x$ and when divided by $b$ has remainder of $y$". Is there a fast way to finding this number?
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0answers
20 views

On a 2-dimensional Van der Waerden-like theorem on 2-coloured square grids

Let us consider a $n\times n$ grid. We colour each point of the grid using two colours. We say that a grid is bad is there exists a set of 4 points on the grid with same color which are the vertices ...
0
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0answers
60 views

Generalization of Captives Wearing Hats puzzle

I have been playing with the following puzzle on and off for a few years, but I haven't been able to address this particular generalization. Background This problem is somewhat involved, so it's ...
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2answers
67 views

What is the missing number in the following sequence? [closed]

$$ 2, 12, 60, 240, 720, 1440, ______, 0 $$ Please explain the logic as well.
1
vote
2answers
122 views

Clock losing time puzzle

The question goes as: A wall clock and a Table clock are set to correct time today on 10 pm. The wall clock loses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour ...
2
votes
2answers
52 views

Validation of Answer via Truth Table as Reason in Isolation

I've tried various google and math.SE search strings but I'm having trouble formulating a query that gives me relevant information. Questions Does this table below accurately represent an acceptable ...
5
votes
2answers
104 views

Expected number of wrong seats on plane

Many people will be familiar with the set up of this problem: you have an aeroplane with 100 seats, and 100 passengers who have been allocated unique seats. The first passenger forgets their ticket, ...
36
votes
6answers
4k views

Drinking habits riddle: the village is $90$%$+80$%$+70$%$+60$%$ = 300$ % saturated with liquids

In a small village $90\%$ of the people drink Tea, $80\%$ Coffee, $70\%$ Whiskey and $60\%$ Gin. Nobody drinks all four beverages. What percentage of people of this village drinks alcohol? I got this ...
9
votes
3answers
235 views

Getting an airplane around the world

I'm interested in a generalization to the following riddle: You're the director at an airport on the equator, and each plane at your airport can hold enough fuel to fly half way around the world. ...
3
votes
0answers
115 views

Explaining MENSA's IQ Problem on Alien Fingers

There is one probably quite well-known IQ puzzle below from Mensa: There are a number of aliens in a room. Each alien has more than one finger on each hand. All aliens have the same number of ...
1
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0answers
188 views

Cyclic Partisan Nim Variant

This game is played with a sequence of heaps and a position marker, where each heap is owned by exactly one player. The game ends when a player has removed all objects from their own heaps, and this ...
13
votes
3answers
2k views

An invisible ghost jumping on a regular hexagon

Given a regular hexagon and an invisible ghost at one of the vertices of the hexagon (we don’t know which). We have a special gun, that can kill ghosts. In a step we are able to shoot the gun twice (i....
11
votes
1answer
120 views

A generalization of the airplane seating puzzle

Let me say immediately that this isn't my puzzle. Someone posted it earlier, and I was working on it when it was deleted. It seems to me to be an excellent puzzle, too good be deleted, so I'm ...
25
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3answers
680 views

Hat 'trick': Can one of them guess right?

There are $n$ boys and $n$ girls. Each of them is given a hat of only 4 possible (known) colors and doesn't know its color. Now each can only see all the colors of hats of those of the other gender ...
10
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5answers
235 views

9-Bits Game, a Brain Teaser on Information Theory or Cryptography

This question was asked in a recently interview, I didn't solve it. Suppose there are two very smart people Alice and Bob, there participate in a game, the game is set as followed. Some ...
5
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1answer
437 views

Arranging bricks safely

The goal is to arrange bricks safely so that there is no line that can be cut through. For example This arrangement is considered unsafe because you can cut through the red line. This is a safe ...
6
votes
1answer
109 views

Garage Door Puzzle

When I drive home, I open my garage door from my truck. I cannot see the garage door until I turn into my driveway. I want to know the range of my opener. How close can I get to knowing the farthest ...
2
votes
4answers
95 views

How many fair dice of this kind exist?

I am not talking about the shape of the dice here, I am talking about another type. You will see what I mean soon. For example, when there are 1 dice, a normal dice is a fair dice, because the ...
5
votes
2answers
107 views

Pirate's Game: What if proposer can't vote

I had read the Pirate's game With other number of pirates and coins we can think the same way But I supposed maximum number of coins that pirate A might get if plan still accepted when get a half ...
17
votes
4answers
2k views

Can all arbuzoids assume the same color?

This puzzle is from a Russian web-site http://www.arbuz.uz/ and there are many solutions to it, but mine uses linear algebra and is very naive. There’s a planet inhabited by arbuzoids (...
8
votes
1answer
150 views

An extension of the Four 4's game

When I was in lower school I remember playing the Four $4$'s game and we got to around $10$. For those of you who don't know the Four $4$'s game is one where you have to use four $4$'s and you have to ...
2
votes
2answers
61 views

Refueling cars on circular racetrack puzzle

Suppose there are a number of cars at the start line of circular racing track with a fueling station. Each car can carries enough fuel to drive exactly half a lap. The cars can either refuel at the ...
0
votes
1answer
31 views

Is the algorithm for determining if an $N\times N$ ($15$) puzzle is solvable the same as $M \times N$?

Most of the algorithms I've seen discuss $N\times N$ grids only. This is the method I'm talking about: An inversion is when a tile precedes another tile with a lower number on it. The solution ...
19
votes
3answers
3k views

Is the aim of this Tic-Tac-Toe puzzle possible to achieve?

I was playing Tic-Tac-Toe with my friend when I came up with a puzzle. I might have to put this on the Puzzling Stack Exchange, but I do not know if the aim of the puzzle can be achieved. I am aware ...
1
vote
1answer
54 views

Probability of painting the whole wall with bars of 1x10 pixel length

Today I faced an interesting question. Let me tell the full story, my colleauge was in an muesum and saw a specific art. The painter was writing words on a wall until the wall was nearly filled up to ...
3
votes
1answer
38 views

A Particular Peg-jumping puzzle

Many years ago I was shown this puzzle. It's a type of solitaire or peg-jumping puzzle. One places some arbitrary arrangement of pieces on a rectangular grid, below the grid dividing line (the bar). ...
2
votes
1answer
94 views

Prove that two sums must be equal among the possible sums of the rows, columns, and diagonals of a $3\times 3$ arrangement of boxes.

A $3 \times 3$ arrangement of boxes is filled with one of the numbers one, seven, or nine. Prove that of the eight possible sums along the rows, the columns, and the diagonals, two sums must be equal. ...