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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.

0
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1answer
25 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....
-3
votes
0answers
42 views

need assistance with my sons homework [on hold]

I am trying to solve one math question for my son. I tried to solve it using google, but could not find the solution. Below is the image of the question: Clock problem I need to find the missing ...
2
votes
2answers
56 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 ...
-2
votes
1answer
52 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
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0answers
49 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. ...
-1
votes
0answers
31 views

Puzzle question [closed]

How can we arrange 8 balls to have 5 balls in a row and 5 balls in a column? This is the original question: 8 balls are arranged as shown below. Move one ball to a new to have a row of 5 balls and ...
0
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3answers
39 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 ...
1
vote
1answer
30 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
30 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 $b$?
2
votes
0answers
50 views

Cutting a Solid Torus with $n$ Planes

Question: How many pieces 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 ...
0
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0answers
23 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
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1answer
45 views

Optimal moves for maximizing perimeter? [on hold]

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 ...
0
votes
1answer
44 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 $...
5
votes
1answer
124 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 ...
1
vote
3answers
49 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
55 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 ...
2
votes
1answer
39 views

Guess the color of the cap - extended

I had here (Guess the color of the cap) the following problem: I have 3 persons which either wear a white or a black cap. They can only see the color of the other caps, but not their own. White and ...
3
votes
0answers
74 views

A coding theory/probability puzzle

I thought of the following problem and I am stuck in solving it. Suppose there is a deck of 4 cards with 2 red and 2 blue. I pick 2 cards at random and choose 1 and show the other to my friend. With ...
1
vote
1answer
47 views

What numbers should I not pick?

I have a problem on my hands and I am a little confused on how to solve it. Say you have $50$ people and each chooses a number from $0$ to $100$. Now you take the average of all the numbers and ...
1
vote
0answers
63 views

n hats/boxes problem [closed]

Do anyone have a clue about the below problem: A set of n persons with a distinct hats tagged accordingly by $1,...,n$ leave their hats in a room and leave the room. A naughty boy then take the ...
0
votes
0answers
30 views

Faulty logic-related proof - what goes wrong?

I was on /r/math the other day and I saw a "proof" that interested me. I slightly modified it to make it less convoluted. Consider the statement "the smallest natural number that is not described by ...
0
votes
0answers
17 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 ...
1
vote
2answers
54 views

Guess the color of the cap

I have 3 persons which either wear a white or a black cap. They can only see the color of the other caps, but not their own. White and black caps are eqally likely. As a team, they play a game of ...
2
votes
3answers
1k views

How to solve a large system of linear algebra?

A friend has given me the following puzzle to solve, however, I lack the linear algebra knowledge to calculate the solution, and my attempts to brute force the solution have been foiled by a large ...
3
votes
1answer
79 views

GCD Euclid's algorithm as solution to the 2-buckets water puzzle

I completed an exercise on HackerRank, a site for programming exercises. The problem has been inspired from Die Hard 3 movie. The original problem is like the following. The problem You are given ...
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votes
1answer
112 views

If $5 * 5$ = $10$ , $6*6$ = $18$ , $7*7$ = $36$ ; then $7* 8$ =? [closed]

If $$\quad 5 * 5 = 10$$ , $$\quad 6*6=18$$ $$\quad 7*7=36$$ then $$\quad 7* 8 = ?$$ a) $54 \quad$ b) $51 \quad$ c) $30$ NOTE: Here '$*$' is not simple multiplication It is some logic or ...
0
votes
1answer
68 views

If $\, 5$ & $4\to 100$ , $8$ & $5 \to 400$ , $2$ & $19 \to 361$ , $A$ & $5 \to 625$ , $12$ & $3 \to 324$ , $7$ & $6 \to 441$ ; then $A=?$

Suppose it is given : $\quad \, 5$ & $4\to 100$ , $\quad 8$ & $5 \to 400$ , $\quad 2$ & $19 \to 361$ , $\quad A$ & $5 \to 625$ , $\quad 12$ & $3 \to 324$ , $\quad 7$ & $6 \to ...
4
votes
4answers
69 views

Number of ways the room can be tiled with $I$ shaped and $L$ shaped tiles

There is a room of dimension $2\times 12$ units. You have to tile it. There are two types of tiles: I-Shaped - it is of a dimension $1\times 2$ units, L-Shaped - it is in the shape of $L$ which has ...
8
votes
2answers
137 views

Can this puzzle be solved mathematically?

There are $6$ people in a ship. As the journey is long, they decide to take shifts. In each shift, some wake up and control the ship while others sleep. How many such shifts are required so that for ...
0
votes
2answers
48 views

How to compute the different number and ways to read a given phrase forming a pile or a stack?

I'm totally lost in this riddle, does it exist a way to calculate the different ways to read a word using a systematically approach?. In my initial attempt what I tried to do is drawing a circle over ...
0
votes
0answers
32 views

Valid Megaminx Patterns

A Megaminx is a dodecahedral twisty puzzle similar to a Rubik's cube. Each of the twelve faces has a different color; the puzzle is cut into 50 pieces by slices parallel to the faces, which may be ...
0
votes
1answer
42 views

How to solve this problem raven matrices problem?

I am doing this free test in http://test.mensa.no/ That, as far as I know, the only problem I can't solve. Basically we shift the first row to the right. From first to second is easy transformation. ...
4
votes
3answers
150 views

Minimum number of steps in water measure problem

I've been struggling with this problem for a while and gone through questions about the "Water Jug Problem/Puzzle". A person wants to have $2$ separate $1$ L measures of water at the same time. ...
2
votes
3answers
77 views

Two doors, each either trapped or safe, have signs whose truth depends on certain circumstances. Each sign reads “Both doors are safe”.

A friend of mine sent me the following puzzle: There are two doors, and behind them either a trap, or a safe passage to somewhere, and on the doors, it is written something about whether the ...
1
vote
0answers
41 views

Stacked Conditional densities

I am struggling on the following problem (altered for better understanding): Let's say the height of a father $x_F$ is drawn from a normal distribution $X_{F} \sim \mathcal{N}(\mu,\sigma_F^2)$ and the ...
0
votes
2answers
49 views

puzzles of probabilities

A grandmother is cleaning out her garage and finds 6 items that she no longer wants to store. She has two charities that she likes to donate to, so she is going to put the 6 items into two boxes. ...
1
vote
1answer
40 views

What's the probability that picking $3$ coins from a bag containing all coins from $1$ cent through $2$ euro will yield a total of $80$ cents?

I recently ran into this interview question and am wondering if my solution is correct. The setting is We have a bag containing one coin of each type, i.e. we have one $1$ cent coin, one $2$ cent ...
2
votes
3answers
53 views

Is it possible to know the result of a match between three teams with only knowing their goals for and goals against?

I've found this problem in my book and left clueless on how to make the right interpretation to come up with a solution. The situation involves a hockey match. Typically when you have a goals for and ...
0
votes
1answer
49 views

How to find the number of different existing routes in a problem where there is a maze of interconnecting lines?

I had to solve this riddle from my book but so far I'm stuck at by doing several attempts and I felt it is like counting grains of sugar or some kind of sisyphean task. Can somebody help me with this? ...
0
votes
1answer
44 views

Recompute expected value of the sum of value of five face down cards when the lowest value card is replaced by a new face down card

Recently I heard of this puzzle/riddle type question that was asked in an application interview and I am unable to solve it. The problem is as follows Stage 1: The interviewer holds a regular deck ...
0
votes
1answer
20 views

Does a problem involving finding the least amount of trials in weighing to reach a certain quantity can be solved without derivatives?

I've been going in circles with this kind of problem, hence need some help into trying to find if this kind of situation can be solved without the use of derivatives. The problem is as follows: In ...
3
votes
0answers
71 views

Puzzle (1): Explaining a pattern in multiplication graphs modulo $m$

In the plots of multiplication graphs $\mu^n_m(k) = kn\ \%\ m$ (with $a\ \%\ b$ meaning $a$ modulo $b$) the dots are undeniably arranged along parallel lines with a well-defined common slope $\alpha$ ...
2
votes
1answer
72 views

Puzzle Using Cubes

While playing one day, Megan decided to build cubes out of a box of individual sugar cubes. Megan emptied the box onto the floor and using the sugar cubes as building blocks, Megan made three solid ...
2
votes
1answer
45 views

A game-theoretic chess puzzle — Proof verification

I recently came up with the following chess puzzle (which has almost nothing to do with one's Chess skills): Puzzle: Consider a variant of chess where black has to start with $1...e5$ regardless of ...
3
votes
3answers
97 views

Does there exist a way to simplify or build a table to find the truth in a set of given statements involving 5 individuals?

This problem has got me going in circles for several hours and I'm not sure what to do, the problem is as follows: At a semiconductor laboratory in Hsinchu a security guard caught five ...
3
votes
1answer
47 views

When the numbers $8, 11, 18, 20, 23, 32, 38$ are placed to form an equality in the empty boxes below, which one of the numbers will not be used?

When the numbers $8, 11, 18, 20, 23, 32, 38$ are placed to form an equality in the empty boxes below, which one of the numbers will not be used? I tried to distribute the 4 biggest number ($38+20 +...
2
votes
0answers
51 views

Filling a modified sudoku/latin square

Let us build a square array in the following manner, which I would like to call a modified sudoku: 1) Every row and column contains only one copy of a positive entry and there are exactly $t$ such ...
9
votes
0answers
356 views

$5 \times 5\;$ “square additive set”

Problem: IBM Research - Ponder This - January 2019 monthly contest (which was closed few days ago) leads to the problem: Find sets $A = \{a_1,a_2,\ldots,a_n\}$, $B = \{b_1,b_2,\ldots, b_m\}$ such ...
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votes
2answers
40 views

I give coins to my friend in stages. Why is the total number of coins given not equal to the total of the leftovers at each stage?

Let's say that I have 50 coins, total. I give 20 coins to my friend; I'm left with 30. Then I give 15 more; I'm left with 15. I give 9 more; I'm left with 6. I give 6; I'm left with 0. When I sum-...
0
votes
1answer
90 views

Solve the following riddle

I.As related by the mathematician X, he was once visited by the brothers N, who, upon entering, took off their hats and hung them up on a rack in the hall. Later, when the guests were leaving and ...