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 ...

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0answers
35 views

Tetromino coloring problem on a grid

Problem: All the tiles on an $n\times n$ grid are black or white. Every possible T-tetromino of tiles on the grid is examined. A T-tetromino is 'happy' if has 2 white tiles and 2 black tiles. ...
1
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0answers
33 views

prove that using 10 coins is enough to cover any 10 points in a plane [duplicate]

I recently got this puzzle, cant seem to prove it, i have manage to prove that for large enough N there is no solution, but not for 10. the puzzle asks to prove that using 10 coins is enough to cover ...
0
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1answer
26 views

How many different arrangement are there for $14-15$ puzzle, so that it become impossible to solve?

Sam Loyd's unsolvable $14-15$ puzzle is well known to everyone. I also found it quite fascinating when I was playing with it in my childhood but didn't know about that one particular arrangement that ...
-3
votes
1answer
43 views

A Mathematical Riddle of Averages

The following is an unexpected riddle that originated from the fact that my Calculus teacher enjoys being mean with us, the students: The fact that not all students in a class can be above the ...
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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 ...
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4answers
1k views

Divide by a number without dividing.

Can anyone come up with a way to divide any given x by any given y without actually dividing? For example to add any given x to any given y without adding you would just do: $x-(-y)$ And to ...
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. ...
5
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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
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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, ...
7
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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?
0
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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 ...
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5answers
9k views

Famous puzzle: Girl/Boy proportion problem (Sum of infinite series)

Puzzle In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is ...
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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 : $15$ $2$ ...
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. $$\sqrt{4+\sqrt{4+\sqrt{4-\sqrt{4-x}}}} = x$$
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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" ...
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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, ...
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votes
2answers
893 views

How many different ways can I add three numbers to get a certain sum?

I'm working on a little program and I stumbled across a small math problem I can't quite solve. This is what the program does. A sum is generated. Now, the user can subtract either 3, 4, or 5 from ...
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 ...
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 ...
-1
votes
2answers
71 views

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

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

Not so obvious probability puzzle.

You are given two boxes with a number inside each box. The two numbers are different but you have no idea what they are. You pick one box to open; read the number inside; and then guess if the number ...
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 ...
4
votes
2answers
8k views

Logic Puzzle of the age of three sons

There is a puzzle, it goes something like this: Someone talks to a guy, and asks, Give me the age of my three sons, The other guy asks for some clues: The product of the age of the three sons (of ...
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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 ...
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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 ...
5
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3answers
880 views

How to solve 5x5 grid with 16 diagonals?

I have a grid 5x5 and I have to fill 16 little squares with a diagonal Rules You cannot place more than 1 diagonal in each square The diagonals cannot touch each other (example bellow) Click ...
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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
456 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?
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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 ...
4
votes
4answers
2k views

Some digit summation problems

What is the sum of the digits of all numbers from 1 to 1000000? In general, what is the sum of all digits between 1 and N? f(n) is a function counting all the ones that show up in 1, 2, 3, ...
1
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2answers
687 views

How many balls does he put into each green bag?

This is a homework problem my son brought home -- 5th grade. Raul has 56 bouncy balls. He puts three times as many balls into red gift bags as he puts into green gift bags. If he puts the same ...
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 ...
0
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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?
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1answer
35 views

how to determine the day of the week when some clues are given?

In a year, there are more Mondays than Fridays, and more Sundays than Wednesdays. Which day of the week is the first day in March of that year?
2
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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 ...
0
votes
5answers
5k views

Absolute values of 1-10 in a pyramid form [closed]

_ _ _ _ \/ \/ \/ _ _ _ \/ \/ _ _ \/ _ you have numbers 1-10. you can only use each number once and the number below is equal to the absolute ...
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 ?
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votes
3answers
121 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 ...
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 ...
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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 ...
65
votes
24answers
14k views

Blue eyes: a logic puzzle

Today I read the Blue Eyes puzzle here. I also read the solution which I find quite interesting. But there are three follow up questions which I don't know the answer to: What is the quantified ...
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). ...
-1
votes
3answers
161 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 ...
8
votes
1answer
292 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
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 ...
4
votes
2answers
976 views

Frog Jump Problem

Lotus leaves are arranged around a circle. A Frog starts jumping from one leaf in the manner described below. In the first jump it skips one leaf,next jump it skips two,three the next jump ...