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 ...

learn more… | top users | synonyms (1)

1
vote
0answers
49 views

Ball Colouring problem clarification

Before you downvote this for being a duplicate, kindly take cognisance of the face that I don't have enough reputation to comment on the germane answer.I'll attempt to pose my enquiry as a question In ...
1
vote
1answer
264 views

Logic - truth and lies in a circular table.

Germans lie when talking about Americans, and Americans lie when talking about Germans. Germans tell the truth when talking about Germans, and Americans tell the truth when talking about Americans. ...
8
votes
7answers
3k views

The number of bottles of beer one can buy with $10, after exchanging bottles and caps [closed]

My answer to this question is 15, but my dad insists I am wrong. Who is right? $2 can buy 1 bottle of beer. 4 bottle caps can be exchanged for 1 bottle beer. 2 empty bottles can be exchanged ...
2
votes
1answer
68 views

equation where the numbers don't matter(SOLVED) [closed]

me and my friends are making an escape room and we had the idea of using a pack of Bean Boozled jelly beans (for those not known with them, it is a small box of jellybeans with 10 pairs of flavours, ...
0
votes
1answer
49 views

Prove: In a finite geometry, if a line has $n$ points, then the total number of points is $n^2 - n + 1$.

Prove: In a finite geometry, if a line has $n$ points, then the total number of points is $n^2 - n + 1$. The following axioms define a finite geometry: ...
3
votes
1answer
82 views

A game with stones, sure win strategy?

There are two players. They alternate taking turns to move a stone (only one stone per turn) of their choosing. Stones can be moved only left as far as you want, as long as you don't jump over another ...
0
votes
0answers
54 views

How to find the function?

I need to find a function that takes two integers as input and outputs an integer. Input : $28$ $1$ Output : $68$ Input : $39$ $1$ Output : $90$ Input : $90$ $1$ Output : $81$ Input : $15$ $2$ ...
7
votes
5answers
203 views

A riddle about a liar

Say Alice says:'the probability that I'm lying is greater than p.' What's the probability that Alice is lying?
1
vote
1answer
69 views

Solve an equation with a finite chain of nested radicals

Solving an infinitely long square root problem is easy but how to solve this one? The equation goes like this. $$\sqrt{4+\sqrt{4+\sqrt{4-\sqrt{4-x}}}} = x$$
1
vote
0answers
53 views

Formulation for solving puzzle game mathematically

I'm developing a solver for a simple constraint-based puzzle game. Here is an example of the puzzle: $$\begin{align} - \;6\; -\\ - - -\\ - \;3\; - \end{align} $$ The given 3$\times$3 grid of "clues" ...
0
votes
3answers
35 views

Finding the # of paths in a grid from opposite corner but most avoid certain paths

In x-y coordinate you start out at (0,0) and you want to get to (8,14) by either moving up or right only. You can't move to any points that are both odd, e.g. (1,1), (1,3)... (3,1), (3,3) ... (7, ...
2
votes
4answers
29 views

On Coprime Numbers and Age Differences

Hypothetical Situation: Currently, I am $38$ and my wife is $33$, so this year our ages are coprime. Will our ages always be coprime? (If we happen to have the same birthday, so our age difference ...
-1
votes
2answers
71 views

Riddle: which is the next bigger number? [closed]

How to solve this puzzle? Follow this link
0
votes
1answer
69 views

The puzzle about a country of truth tellers and liars.

I tries to solve a logic puzzle below. It seems $(A \vee \neg A) \wedge B$ is the answer, but I'm not sure. Can anyone give me an answer? A certain country is inhabited only by truth-tellers (people ...
0
votes
1answer
84 views

19 digit prime number?

I am searching for a particular type of prime number. It is of 19 digit.If I removew unit place it will reduce to an 18 digit prime number. If I again remove digit from unit place it will become 17 ...
0
votes
0answers
30 views

Probability of winning a game (Puzzle)

Solving a probability puzzle: Given a two-player game, both players have N K-sided fair dice (N fair dice of K sides each). Each player have an initial score H, a player losses the game if he/she ...
0
votes
0answers
36 views

How soon will these frogs meet?

Thanks to everyone who helped me figure out if two jumping frogs will ever meet. Part 2 of that question (which I was recommended asking in a new post) is how to, in the simplest way, figure out the ...
4
votes
4answers
454 views

How to draw Square Diagonal? [duplicate]

Draw a 5x5 square. In 16 of 25 squares draw diagonals in such a way that no diagonal ends touch. How can I do this?
7
votes
6answers
2k views

Will these frogs ever meet?

Two frogs are on an eternal stairway. Will they ever be able to meet? Anton is on step 14 and jumps 4 steps. Billy is on step 16 and jumps 6 steps. The way I look at this is that as long as they're ...
0
votes
0answers
32 views

Find three ages

Transposing the two digits of A's age gives B's age. The difference between their ages is twice C's age and В is ten times as old as С. What are the three ages? Let A's age be $ab=10a+b$ so ...
0
votes
1answer
17 views

how to determine particular months with five weekends

January of 2016 has five Fridays, five Saturdays and five Sundays. What is the next January that will again have five weekends like this?
1
vote
1answer
61 views

28 soldiers puzzle

A leader ordered his 28 soldiers to protect the castle , the castle has 4 walls or sides. He wants 9 soldiers to guard each wall. How can the be possible ?
2
votes
0answers
49 views

Rifleman game with $n$ players in $D$ dimensions: what is the survivor fraction when $n,D\to\infty$?

This is a follow up to this question where the following problem is explored (for $D=2$): $n$ riflemen are distributed at random points in $[0,1]^D$. At a signal, each one shoots at and kills his ...
1
vote
3answers
44 views

Solution to this limit

Can anyone tell me how to calculate this limit (see below)? It is a puzzle so I think there must be some trick. $$\lim_{x \to \pi/20} \left( {(\sec x)}^{\cos x} + {(\csc x)}^{\sin x} \right).$$ It ...
1
vote
1answer
40 views

How can I calculate the total number of unique solutions for the n queen puzzle?

Constructing a fairly optimized algorithm for finding all the possible solutions for the n queen puzzle is fairly easy, at least for up to 20 queens. Is there a way though to calculate the number of ...
2
votes
2answers
107 views

Very fascinating probability game about maximising greed?

Two people play a mathematical game. Each person chooses a number between 1 and 100 inclusive, with both numbers revealed at the same time. The person who has a smaller number will keep their number ...
-1
votes
3answers
160 views

How old is the captain and ship?

At the time the ship was as old as the captain is now, the captain was twice as old as the ship. Together they are 56 years old. How old is the captain and ship? I've figured out the answer, but I ...
0
votes
1answer
36 views

Maximum multiple of 3 using three numbers and given operations

Given three numbers $a$, $b$ and $c$ find the greatest multiple of 3 that can be formed from these numbers using the following rules and operations. The initial result is $0$ During each operations ...
2
votes
1answer
87 views

Does there exist a tool to construct a perfect sine wave?

For example, a perfect circle can be constructed using a compass and a perfect ellipse can be constructed using two pins and a piece of string, because a circle can be defined as the locus of points ...
0
votes
1answer
26 views

Need way to statistic puzzle

Hello guys i need help with statistic problem. The problem is : In room have 3 doors, one door is exit from room (o minutes) , second is return us to the room after 3 minutes , and last door is ...
6
votes
3answers
120 views

Board game on a $m\times n$ board - winning strategy

Two friends, $A$ and $B$, play a game with one single game piece on a rectangular board with $m$ rows and $n$ columns. $A$ begins the game by moving the game piece from its starting point $(1, 1)$ to ...
2
votes
1answer
77 views

$F(F(x)+x)^k)=(F(x)+x)^2-x$

I have no idea about this problem. But I feel we have to use chain rule of differentiation here. The Function $F(x)$ is defined by the following identity: $F(F(x)+x)^k)=(F(x)+x)^2-x$ The value of ...
-1
votes
3answers
378 views

Seconds of a Clock [closed]

A clock takes 12 seconds to strike 4, how long does it take to strike 12? I have already tried EVERYTHING, but nothing seems to work.
6
votes
1answer
127 views

Deriving the surface area of a sphere from the volume

I am a high school student, so I know how to derive the volume $V=\dfrac{4}{3}\pi r^3$ using calculus, but I am unable to derive its surface area. However, I notice that we can approximate the ...
0
votes
1answer
29 views

Solution to a simple number theory problem (how much)

Bob has $x$ Euro. $x \in [m..n]$ $m, n \in \mathbb{N}$ If Bob were to buy 9 cars costing $c$ each, he would only have 1 Euro left. $x = 9c + 1$ If Bob were to buy 7 boats costing $b$ each, he would ...
1
vote
2answers
155 views

Are all Nonograms / griddlers uniquely solvable?

A Nonogram (also called a Griddler) is a popular puzzle in which you are given a matrix of size $n \times m$ filled with zeros, and you are also given that in row $i$ there are $a_i$ ones and in ...
3
votes
2answers
79 views

Three Proper Ladies on a train [duplicate]

Three proper ladies are traveling on a train. Each turns red within one second if they become aware of dirt on their face. They are too proper to tell the other if they have dirt, and there are no ...
2
votes
2answers
118 views

Probability of at least two daughters in three-child family, given a daughter Mary

Bob and Jane have three children. Given that one child is their daughter Mary, what is the probability that Bob and Jane have at least two daughters? (I am also interested in wordings of this ...
8
votes
1answer
291 views

Best strategy to find a parking lot

New Bounty Edit (2 days remaining on the Bounty): To point out that the only answer given at this time cannot be considered an answer, because it simply gives a hint on how to formally model the ...
0
votes
1answer
28 views

Probability of scoring positive in a certain test .

In a math contest problem appeared which I have trouble solving . It goes as under - Consider an examination of $N$ questions - fully multiple choice questions . There are $c$ choices for each ...
10
votes
1answer
425 views

Systematic solution to my soccer ball puzzle

I once received a puzzle that can be described as follows: There are $12$ black pentagonal and $20$ white hexagonal pieces. The goal is to form a soccer ball from these (aka. truncated icosahedron). ...
0
votes
2answers
110 views

$1$ man can eat $1$ apple in $1$ day.How many apples can six men eat in six days?

$1$ man can eat $1$ apple in $1$ day.How many apples can six men eat in six days? My approach: $1$ men can eat $1$ apple in $1$ day. Now, 6 men can eat in 6 days 6 apples only assuming each men eat ...
0
votes
1answer
26 views

What fraction of the job can be done by one man in one day given 10 men can do a job in 10 days?

If 10 men can do a job in 10 days.What fraction of the job can be done by one man in one day? My Approach: $10$M . $10$D=$100$MD ($10$ men take $10$ days =$100$ man days) $1$ . $1$=$1/100$ (i.e ...
0
votes
1answer
69 views

Interesting Original Probability Question

I have 100 balls, which are all initially yellow. Every minute, I randomly choose a ball and paint it red. How many balls are expected to be red after 100 minutes? Note: I could pick up a ball that's ...
5
votes
3answers
312 views

Alice's Adventures in Wonderland

Excerpt from Lewis Carroll's book: "Let me see:four times five is twelve,and four times six is thirteen,and four times seven is-oh dear! I shall never get to twenty at that rate!" My questions: ...
2
votes
1answer
97 views

Shortest path between two points on graph?

A graph has 100 vertices. Each vertex is connected to exactly 10 other vertices such that the whole graph is connected. If I choose two random vertices of the graph, what is the length of the shortest ...
0
votes
0answers
41 views

Number of meetings needed for everyone to know everyone

There are 100 people on an island. Each person has an unlimited number of name-tags with his name on it. (Everyone has a different name) When two people meet, each gives the other an unlimited number ...
0
votes
2answers
50 views

Question about the average number of cycles?

I have 100 cards labelled from 1 to 100. I place this in a row with all the cards face down. On the first turn I flip the first card. Now this card has a number $n$ on it. I then put this card face-up ...
43
votes
3answers
1k views

Expected number of people to not get shot?

Suppose $n$ gangsters are randomly positioned in a square room such that the positions of any three gangsters do not form an isosceles triangle. At midnight, each gangster shoots the person that is ...
1
vote
4answers
76 views

Making a 3x3 magic square that adds up to 1

I got this problem from my sister in 6th grade. I spent 3 hours on this and couldn't figure it out for the life of me. You're given an empty 3x3 square. You have to fill it with numbers from -9 to 9. ...