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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12
votes
1answer
238 views

How can one determine the chess configuration that maximizes the number of possible moves?

To clarify, what is the chess-board configuration that would maximize the number of valid moves one player could make on his or her turn? I thought of this question while playing chess, how apropos. I ...
3
votes
2answers
912 views

Probability Question relating prison break

I am stuck in a question regarding a prisoner trapped in a cell with 3 doors that actually has a probability associated with each door chosen(say $.5$ for door $A$, $.3$ for door $B$ and $.2$ for door ...
4
votes
2answers
254 views

Wolves and chicks puzzle

This problem is from the handheld video game, Professor Layton and the Curious Village. I think the solution is very cool, but more than that, I want to know how to show that the minimum number of ...
4
votes
4answers
1k views

Number system - sum of two digit numbers

The sum of four two digit numbers is $221$. None of the eight digits is 0 and none of them are same. Which of the following is not included among the eight digit ? $$(a) \;\;1 \\ (b)\;\; 2 \\ ...
0
votes
1answer
147 views

How to calculate Team Strength for future prediction?

You are given with $4$ players name, namely Player $A$, Player $B$, Player $C$ and Player $D$. These players are grouped into two teams with two players each. A Game is played between the two team.For ...
6
votes
3answers
926 views

Why does the infinite prisoners and hats puzzle require the axiom of choice?

Infinite prisoners puzzle. The link to Wikipedia describes the puzzle, and the solution. The axiom of choice is used to pick a sequence from each equivalence class, which the prisoners memorize ...
0
votes
1answer
311 views

LOVES+LIVE=THERE. How many “loves” are “there”?

This is a problem from Mathematical Circles ( Chapter 0, Problem#17 ). It goes like this:- The answer is that there are 95343 "loves" in "there". Now, this is something that I am unable to ...
3
votes
1answer
581 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 ...
6
votes
2answers
935 views

Fun Math Topics, Activities, and Riddles

I'll be teaching college algebra this summer. Last summer when I taught the same course, I finished lectures early (thanks mainly to LaTeX's Beamer package). I want to fill these gaps this time ...
3
votes
1answer
404 views

line of mathematicians guess their own hat color out of c colors

There is a common problem in which a long line of N mathematicians are each given a hat that is either red or blue. They cannot see their own hat but can see all in front of time and can hear any ...
4
votes
4answers
1k views

How to calculate the number of pieces in the border of a puzzle?

Is there any way to calculate how many border-pieces a puzzle has, without knowing it's width-height ratio? I guess it's not even possible, but I am trying to be sure about it. Thanks for your help! ...
6
votes
3answers
645 views

Using the digits $7,7,7,7,1$ and the operators $+,-,*,/$ to make a formula which equals $100$

I know the answer is $(7+7)*(7+(1/7))$ or a more ghetto answer is $177-77$. I'm not interested in the answer, more in the problem itself. What is the name of this class of problem? Is there a ...
1
vote
2answers
156 views

Interesting and irritating problem.

How to deal this problem. I found this problem in math competation in 2012. But, I could not solve. Could you help me... Uncle John has taken blood pressure drops for a long time according to the ...
8
votes
1answer
381 views

Bodyguards and Laser Beams

Suppose you are a point in a square room. The walls of the room are mirrors, and there is a man with a laser gun standing somewhere else in the room. The man is also a point, and both of your ...
5
votes
3answers
1k views

programming brain teaser

Given a programming language where you could make as many variables up as possible and you could only perform these three operators find b-1. ...
1
vote
2answers
174 views

Easy Probability Problem

I was told the following probability problem: While doing a math problem today at the contest the probability of Annie, Tom and Karen getting the problem correct first is 1/7, 1/2, and 5/14 ...
3
votes
3answers
2k views

Missing dollar problem

This sounds silly but I saw this and I couldn't figure it out so I thought you could help. The below is what I saw. You see a top you want to buy for $\$97$, but you don't have any money so you ...
2
votes
1answer
95 views

How many unique rotating sequences?

This is a small puzzle I've been playing with for the past couple of days: For some length N, how many unique sequences of digits can be created when any 'rotation' of the digits is considered as the ...
6
votes
4answers
137 views

Shortest string possible

I was at an interview, and I was asked to give the shortest string generated given this context free grammar. I did not review in years, so I think I got it wrong. What is the answer so I know it for ...
1
vote
1answer
185 views

Would I be able to use mathematics to prove properties that would help me solve this series of puzzles?

I realise that this may be a little different from most of the questions you get on math.stackexchange, so for that I apologize. I also apologize if there's no "one right answer" given the way I've ...
10
votes
3answers
472 views

What is the least amount of questions to find out the number that a person is thinking between 1 to 1000 when they are allowed to lie at most once

A person is thinking of a number between 1 and 1000. What is the least number of yes/no questions that we can ask and know what that person's number is given that the person is allowed to lie on at ...
3
votes
2answers
200 views

Checking Sudoku - sufficient sums

Are the following condition sufficient for checking if solution of Sudoku with (extended output) is valide : sum of values in each row, column and subsquare is equal to 45 and sum of squares of ...
4
votes
1answer
110 views

creating a more complex sudoku (69x6)

I would like to know if its possible to create a "sodoku" with this rule: in a table $69\times 6$ i want to put in the numbers from $1$ to $46$ repeated $9$ times, each numbers HAS to stay in the same ...
3
votes
2answers
496 views

Permutation of 1…9 with no ascending or descending subsequence of length 4

Arrange the numbers $1,2,...,9$ in such an order that no four of them appear (adjacently or otherwise) in ascending or descending order. Show that there is no arrangement of the numbers $1,2,...,10$ ...
2
votes
1answer
622 views

The minimum number of mice required to find a poisoned bottle.

Here's an interesting question. There are $1000$ mice and $1000$ bottles (numbered $1,2,3....1000$). One of the bottles is poisoned. You can mix the solution with the other bottles any number of ...
0
votes
1answer
185 views

Where is the logical error in this Math question? when it say where is the remaining 1? [duplicate]

Three person buying something by 30, each pay 10, after a while, the owner making a discount of -5, but he realize that 5/2 is not good, so, he will return 1 for each, and gives the remaining (2) to ...
3
votes
1answer
309 views

n-bucket water puzzle

Inspired by this post. I am thinking of a general case. Reference to read. Suppose $N,L_1,L_2,p,q$ are integers, and $N L_1 = pq$. with $p\ge 2$ and $L_1>L_2$. Now you have $N+1$ buckets, the ...
4
votes
1answer
3k views

Three bucket water puzzle

You have three buckets, two big buckets holding 8 litres of water each and one small empty bucket that can hold 3 litres of ...
4
votes
2answers
399 views

Tangential quadrilateral

I just proved that "In every tangent quadrilateral the sums of the lengths of opposite sides are qual. Conversely, every quadrilateral with this property is a tangent quadrilateral". Now I am a ...
4
votes
2answers
231 views

A puzzle on knotted surfaces

Only after having learned that the somehow only notion of equivalence of knots is definitely "ambient isotopy" I stumbled over this blog entry on ambient isotopy. (Had it been earlier!) What bothers ...
1
vote
2answers
374 views

Slide Puzzle logic??

say there is an image made into a slide puzzle in a grid of sections 4 wide and 6 high, the missing piece that is missing so you can slide the other pieces of the puzzle around is always the bottom ...
1
vote
1answer
548 views

Gödel, Escher, Bach: $ b $ is a power of $ 10 $.

I’d like to verify if my formula correctly expresses that a number is a power of $ 10 $, using the $ \sf{TNT} $ language provided by Hofstadter in his famous book Gödel, Escher, Bach: An Eternal ...
18
votes
3answers
2k views

Why should Rubik's cube get attention from mathematicians?

I've seen a lot of math debate, calculations and other stuff related to Rubik's cube lately, but I don't really understand why is it important, why should anyone spend time asking and answering ...
3
votes
1answer
126 views

Acute triangle problem

I read this in a maths magazine once, but never quite got the answer. You are given a right-angled isosceles triangle. You need to draw in straight lines to form acute triangles, until you are left ...
5
votes
2answers
152 views

How many cups of sugar do I need for these 5th grade problems?

Problem 1a: If 4 glasses of a mixture needs 1 cup of sugar how many cups of sugar are needed for 5 glasses? This one is easy and makes sense. It's just simply $\frac{1}{4}*5$ Now taking it a notch ...
3
votes
2answers
867 views

Villager Logic Puzzle

Each inhabitant of a remote village always tells the truth or always lies. A villager will give only a “Yes” or a “No” response to a question a tourist asks. Suppose you are a tourist visiting this ...
2
votes
2answers
117 views

Puzzle: Arranging a stack of spheres

Lets say we are arranging a stack of spheres in this manner: To place a sphere over other spheres one needs atleast 3 spheres below it to support it . When one brings 3 spheres together one can put ...
5
votes
1answer
61 views

Proving upper limit on number of moves?

In a $(2n-1)\times(2n-1)$ square grid every small square is marked with Up or Right or Down or Left arrow. An example would be $$\begin{array}{|c|c|c|}\hline\\\leftarrow & \rightarrow & ...
45
votes
1answer
1k views

A discrete math riddle

Here's a riddle that I've been struggling with for a while: Let $A$ be a list of $n$ integers between 1 and $k$. Let $B$ be a list of $k$ integers between 1 and $n$. Prove that there's a non-empty ...
6
votes
2answers
274 views

How to solve this puzzle?

There are $N$ consecutive doors. Two players 'B' and 'J' plays a game. Both take turns alternately, and in each turn a player can open any one door. They define a block of 3 consecutive open doors as ...
1
vote
1answer
142 views

Different number of apples are given to five children such that any $3$ receive more apples than the remaining $2$

A friend asked me this: A woman gave a different number of apples to each of her five children. Any three of her children together received more apples than the remaining two children. What is the ...
1
vote
1answer
549 views

What is the minimum number of moves of solve the puzzle?

There is board in which there are $m\times m$ boxes each assigned an a non zero integer except one box which is marked as $0$ and is treated as vacant. Only the vertical and horizontal neighbors of ...
0
votes
2answers
460 views

Bookshelf problem

There is this thought problem I've been trying to solve, it goes as follows Imagine a bookshelf with a finite number of books in it, to which a finite number of people have access. Each person has a ...
0
votes
2answers
446 views

Clock puzzle.. Bit tricky

Twin Sisters A and B bought 2 wristwatches at 12 p.m . An Hour later , A's watch reads 1:02 p.m while B's watch reads 12:56 p.m. Later , on same day : If A's watch reads 10 p.m then at that time ...
1
vote
2answers
481 views

Burnside's Lemma application

I am trying to understand the Burnside's lemma in order to use it in an example but all my efforts are in vain. The example is as follows: Cards are to be constructed from equilateral triangles, ...
3
votes
2answers
3k views

How to check if a 8-puzzle is solvable?

I have a 8-puzzle 1|2|3 -+-+- 4|5|6 -+-+- |8|7 How can be checked if the puzzle is solvable? Wikipedia states that it is solvable, but does not prove it. Can ...
3
votes
1answer
783 views

Correct Path To Castle Riddle [duplicate]

I'm working on the following riddle that I found to be kind of interesting, but I can't figure it out. The problem is as follows: A prince visits an island inhabited by two tribes. Members of one ...
4
votes
2answers
398 views

Elementary Set theory question … it was asked in Exam

There are $21$ people. $9$ eat dish $A$ $10$ eat dish $B$ $7$ eat dish $C$ $5$ eat dish $A , B$ and $C$ How many people eat at least two dishes? Answer: $10$ (given in solutions) $15$ ...
0
votes
3answers
82 views

Problem related to a given diagram

I came across the above problem but do not know how to tackle it. Can someone point me in the right direction? Thanks in advance for your time.
2
votes
2answers
624 views

Sodoku Puzzles and Propositional Logic

I am currently reading about how to solve Sudoku puzzles using propositional logic. More specific, they use the compound statement $\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,j,n)$, ...