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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5
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3answers
339 views

paper punch puzzle

I was told this lovely puzzle recently which I thought people here might enjoy. Consider a paper punch that can be centered at any point of the plane and that, when operated, removes from the plane ...
14
votes
4answers
1k views

What's the smallest number that we can multiply with a given one to get the result only zeros and ones?

I have the following set of numbers, $$4, 198, 4356, 10296, 14454, 25542, 31779, 51252, 53946, 99999$$ Let's take $3,4$ as an examples: The smallest number to multiply with $4$ to get the result ...
9
votes
0answers
68 views

Solving general (dis)entanglement puzzles

What is the state of the art in (modelling and) solving a general (dis)entanglement puzzle? The following picture shows a nice example: There is a project called "The Untangler", which seems to be ...
2
votes
2answers
576 views

Solving Rubik's cube and other permutation puzzles

I've seen two questions on solving the Rubik's cube but none of the answers have given a complete solution using mainly mathematical techniques. Furthermore, I've not seen a good explanation of ...
5
votes
3answers
96 views

Find a way out in $8 \times 8$ square

Here is one of the mathematic contest problem that my teacher has given me. He said me to solve or find the reason why it cannot be solved. But I was not able to do it. And my searches for similar ...
1
vote
2answers
63 views

What is the fair price of the game below?

You are playing a fair die game with 'n' die rolls. You have decided on the "fair" price of the game. So, to take part in this game you need to pay upfront this value. Then you get to roll a die, n ...
5
votes
1answer
262 views

How many points you should draw in the square at least?

There is a square, which side length is $2$, To ensure there exists a triangle in the square, with an area less than $0.5$, how many points should you draw in the square at least. the goal is for all ...
1
vote
3answers
82 views

Confusion about triangle formation.

A stick of unit length is cut in three parts. Whats the probability that it'll form a triangle. The condition which i used $x_2+x_2\geq x_3$ where they denote sides but i get probability as $\infty$ ...
4
votes
1answer
68 views

Difference Puzzles

I have a puzzle calendar that features 20 or so different types of puzzles. Some are pop culture references and some are logical. Anyway I can do most of the logical ones without breaking a sweat in ...
12
votes
12answers
2k views

A proportionality puzzle

My professor gave us this problem. In a foreign country, half of 5 is 3. Based on that same proportion, what's one-third of 10? I removed my try because it's wrong.
5
votes
1answer
33 views

Manipulation with strings riddle.

Starting with the "string" $PI$, can I or not transform it into the "string" $PK$ by applying the following rules (each rule can be used any number of times, in any order, and $x$ and $y$ represents a ...
5
votes
3answers
132 views

Dwarfs over a bridge

300 dwarfs go over a bridge in the middle of the night. The bridge is rickety and manages at most two dwarfs at a time. With them is a lantern that they must provide at each transition. Dwarfs need ...
1
vote
1answer
51 views

Puzzle: What is the algorithm for finding the kangaroo

There is a kangaroo that placed somewhere on $L$ upon the axis of the natural numbers. At some point of the time, The bell is ringing and the game starts: Each round the kangaroo jumps $K$ steps ...
3
votes
0answers
79 views

Tablecloth & table problem

Friday night we threw an house warming party and invited quite a number of fellow students. To fit everybody around the table we had to enlarge it, pulling out two sort of shelves from the short ...
0
votes
2answers
102 views

Find the number to replace the question mark in between two pairs of numbers

Here is the problem: I have to find the number to replace the question mark. I know there is a series or a pattern to find it any hint will be very helpful.
1
vote
1answer
48 views

Probability Of Two Boys Puzzle (Standard vs Tuesday Boy)

For those that aren't familiar with Gary Foshee's probability puzzle/paradox from 4-5 years ago, you can find an analysis here: http://news.bbc.co.uk/2/hi/programmes/more_or_less/8735812.stm While ...
4
votes
1answer
108 views

What is the minimum number of squares to be drawn on a paper in order to obtain an 8x8 table divided into 64 unit squares? [closed]

What is the minimum number of squares to be drawn on a paper in order to obtain an $8\times8$ table divided into $64$ unit squares. Notes: -The squares to be drawn can be of any size. -There ...
10
votes
3answers
11k views

Finding the n-th lexicographic permutation of a string

I have an ordered set of symbols S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }. I want to find the 1,000,000-th permutation in lexicographic order of S. It is a programming puzzle, but I wanted to figure out a ...
1
vote
2answers
91 views

A number with 6 distinct digits which get multiplied by 5 if we move the last digit to front [closed]

There is a number with 6 different digits, if we pick the last digit of that number and place before that number we got $5$ times our number. How to find such a number?
2
votes
1answer
66 views

Puzzle about sorting coins while blindfolded

You have $n$ coins in front of you, and you are blindfolded. You know that exactly $10$ of the coins are showing heads, the rest are showing tails. How can you sort all the coins into two piles such ...
5
votes
1answer
91 views

How many $9\times 9$ squares can I cut from this figure (it's $38\times 40$ without some corners)

Can I cut 16 ones (along the grid)? I've tried to paint some $15$ cells so that every $9\times 9$ square contain only $1$ painted cell (so I prove there can't be $16$), but to no avail. The figure ...
2
votes
1answer
55 views

About a “99 similar and 1 not similar” problem

A great friend of mine recently sat for an interview. He was asked a question which has fascinated me since some days now. It is Consider you have 100 balls which look the same but one out of ...
1
vote
1answer
47 views

Probability: finding the minimum draws required.

There is a basket filled with $24$ balls. Half of them are red and half are blue. person $X$ draws a ball from the basket wearing a blindfold. what is the MINIMUM number of balls $X$ needs to draw in ...
1
vote
2answers
128 views

I want to write a Christmas message only with particular zeta values. It is possible?

I want to write a Christmas message to leave as a comment thanking the people who in the next 24th December will solve some of my problems: I wish you Math Christmas and a Happy New Year ... ...
4
votes
2answers
172 views

Seeing a pattern (puzzle) [closed]

Does someone see a pattern?: 1 11 21 1211 111221 312211 13112221 1113213211 31131211131221 13211311123113112211 111312211331121321113212221
3
votes
1answer
5k views

Riddle (simple arithmetic problem/illusion)

I'm not sure how well known this "riddle" is but here it goes. 3 people go to a restaurant, each buy food worth 10.00. When they're done, they give 30.00 to the waitress. She gives the money to the ...
6
votes
4answers
27k views

What is the highest number that can be got from 4383 by moving exactly 2 matches?

What is the highest number that can be got from 4383 by moving exactly 2 matches? Number 1 has got 2 matches, so I thought it will be 47831 as I remove two matches from second number (3), but it ...
3
votes
5answers
3k views

How many faces does the resulting polyhedron have?

Take a regular tetrahedron of edge one. Also take a square-based pyramid, whose edges are all one (therefore the side faces are equilateral triangles of same size as the faces of the tetrahedron). ...
6
votes
3answers
208 views

What are good ways of understanding a permutation group from a set of generators?

I'm trying to understand the structure of a Rubik's Cube-style puzzle I'm playing with; I have an expression of the solutions as the permutation group generated by four elements of $S_{16}$, each a ...
2
votes
1answer
77 views

Pick a number that is better than your friends

Consider the following game. There are $n$ players, each one has to pick a (real) number $x$ between $0$ and $100$. There is one round to the game. The winner is the person whose number is closest ...
1
vote
1answer
352 views

How I got this answer

Well i am new to this forum but old to stack exchange but i don't know much about mathmatics tags so sorry for the wrong tags if any. I have a question, but i want to know how i got its answer as 'D' ...
0
votes
4answers
3k views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...
0
votes
0answers
36 views

Puzzle question (trick)

Is there a way to proof that this always works: Pick 21 different cards; Choose one card, and remember it; Place the cards on three accumulations (every accumulation is 7 cards); Choose the one with ...
0
votes
1answer
57 views

2-player game, putting coins on a round table [duplicate]

Two players place coins of identical size (say quarters) on a round table. Each player has to place exactly one coin on the table without overlap with the coins already on the table. The first player ...
22
votes
9answers
5k views

Is Lewis Carroll's reasoning correct?

A bag contains 2 counters, as to which nothing is known except that each is either black or white. Ascertain their colours without taking them out of the bag. Carroll's solution: One is black, and ...
1
vote
2answers
162 views

Eric has got 1 sum wrong

Eric has got 3 sum wrong each time he exactly pressed one wrong key \begin{align} 5+3+2 & =317 \\ 25+36 &=900 \\ 8+8+2 &=3 \\ \end{align} can you work out which key he actually pressed
6
votes
1answer
154 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 ...
6
votes
7answers
3k views
0
votes
1answer
74 views

Is it worth playing this game of dice?

We pay $\$42$ so we can throw $3$ fair $6$ sided dice. We get back the product of the resulting dice values. Is it worth playing this game? What is the expected value of your winnings (or losings) ...
2
votes
3answers
2k views

Seating Arrangement puzzle.

Not sure if its a correct place to post these kind of questions. Eight persons-P,S,Q,R,U,B,J and C are sitting in a field in a circle. Three are facing opposite side and other five are facing the ...
1
vote
0answers
30 views

Concrete solution to the (oriented) Oberwolfach problem with one table

The oriented Oberwolfach problem (with only one table) and its solution are the following. In a meeting of $n$ people during $n-1$ days (combinatorists at Oberwolfach for concreteness), they all have ...
0
votes
1answer
37 views

How to obtain fair competition between two teams

Consider a class with $4$ students having min goals as $\big\{ 1, 3, 4, 5 \big\} $ and max goals as $\big\{ 2, 5, 8, 6 \big\}$. Find the best way to divide the class in such a way that the match is ...
1
vote
1answer
37 views

Logic puzzle, numbers on the back of head

Ok, I found this puzzle and I can't figure out the answer: Two people, Albert and Bernard have a natural number {0,1,2,3 ...} on the back of their heads. Rules: They can't see their own number ...
1
vote
3answers
1k views

Coin Arrangement Puzzle

Disclaimer: I'm not sure how math related this puzzle is (it could potentially be), but I thought it was an interesting puzzle, and I also don't know how to solve it so I wanted to see if anyone had ...
3
votes
2answers
51 views

Find an example of a non trivial Think of a number game

Everyone knows the game where someone ask you to think of a positive integer, then ask you to do some elementary mental operations and finally predict the result. Example: think of a number $n$, ...
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
vote
2answers
2k views

what is maximum number of points of intersection between the diagonals of a convex octgon?

What is the maximum number of points of intersection between the diagonals of a convex octagon (8-vertex planar polygon)? Note that a polygon is said to be convex if the line segment joining any two ...
2
votes
0answers
89 views

When solving a big Rubik cube (100x100x100), do you reduce the solution to like 50x50x50, and then 25x25x25, and then like 10x10x10 and then 3x3x3?

My question is about Rubiks cube. Say you're solving a 100x100x100 cube (you can see examples in youtube by computer program - https://www.youtube.com/watch?v=0cedyW6JdsQ) When solving a big Rubik ...
1
vote
1answer
90 views

Guessing larger of two numbers given finite range

A small twist on the classic probability puzzle: You are given two boxes with a number inside each box, each of which ranges from [A, B]. The two numbers are different but you have no idea what ...
4
votes
0answers
203 views

Geometry puzzle - Show that $x = y$ [closed]

Problem In the following figure, show that $x = y$. My attempts Sadly nothing of value. I have far too little experience with geometry to even begin trying to solve this.