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
2answers
65 views

A Problem Involving Two Sentries

Consider two sentries that are patroling on a road that is 2 miles long. They are sent to points chosen independently and at random on the road. I want to find the probability that the sentries will ...
3
votes
2answers
148 views

Jeep problem variant: cross the desert with as much fuel as possible

I'm dealing with the following variant of the well-known Jeep problem: A 1000 mile wide desert needs to be crossed in a Jeep. The mileage is one mile / gallon and the Jeep can transport up to 1000 ...
0
votes
2answers
29 views

Combine different denominations to form a sum

I am trying to do the Euler Project Problem 31 by hand. ( https://projecteuler.net/problem=31 ) Basically, I am asked how many ways I can form 200 pence by using the denominations 200, 100, 50, 20, ...
4
votes
4answers
3k 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 its width-height ratio? I guess it's not even possible, but I am trying to be sure about it. Thanks for your help! ...
4
votes
4answers
7k views

What is the name of the logical puzzle, where one always lies and another always tells the truth?

So i was solving exercises in propositional logic lately and stumbled upon a puzzle, that goes like this: Each inhabitant of a remote village always tells the truth or always lies. A villager will ...
1
vote
2answers
54 views

What is the value of $xyz$?

Given an expression as : $$xyz+xyz+xyz=zzz$$ where $x,y,z$ are integers and $xyz$ represents a number for example $236$ (not to be confused with $x\times y\times z$), what is the number $xyz$?
1
vote
5answers
5k views

Find a possible pair of numbers given HCF and a factor of the LCM

I was just going through a GCSE paper with a student and I came across a question that I'm struggling to find a good method for. The question was this: Martin thinks of two numbers. The ...
2
votes
3answers
69 views

How can one solve the tower of hanoi problem if there are discs of similar width in it?

For example a line with '1111' represents a disc with diameter of length 4. Similarly a line with '111' represents a disc with diameter of length 3. Below is the representation of a tower that has 5 ...
9
votes
2answers
70 views

Sudoku grid guaranteed to be solvable?

I want to generate random sudoku grids. My approach is to fill the three 3x3 groups on a diagonal of the grid, each with the numbers 1-9 randomly shuffled. That looks e.g. like the grid below: ...
-2
votes
2answers
88 views

If $a,b,c$ are positive and integers, $a+\frac{1}{b+\frac{1}{c}}=\frac{25}{19}$, then $a+b+c=?$ [closed]

I've found this question and tried to solve it, but failed If a,b,c are positive and integers, $a+\frac{1}{b+\frac{1}{c}}=\frac{25}{19}$, then $a+b+c=?$ and how to get it?
5
votes
1answer
3k views

Apparent paradox for the bird traveling between two trains puzzle

Gretings. Trying the "hard solution" for the puzzle below (which has been discussed, with a different angle, elsewhere on this forum) I got to a point where I have three seemingly valid solutions, ...
0
votes
1answer
162 views

Maths Puzzle - Logic

Somebody asked me this puzzle, but they don't have answer to it. 1+2+3+4 = 61 2+3+4+5 = 52 3+4+5+6 = 51 4+5+6+7 = 50 7+8+9+10 = ? I want to know whether my reasoning and ...
1
vote
0answers
30 views

Proof to Theorem 3 in 'A modern treatment of the 15 puzzle' by Archer

I'm reading 'A modern treatment of the 15 puzzle' by Archer and cannot understand the proof to Theorem 3 and how they compute the permutation equation with their examples. My main problem is this ...
2
votes
1answer
47 views

Variant of “prisoners and hats” puzzle with more than two colors

There are $n$ prisoners and $n$ hats. Each hat is colored with one of $k$ given colors. Each prisoner is assigned a random hat, but the number of each color hat is not known to the prisoners. The ...
1
vote
0answers
19 views

Oscillations in a Discrete Dynamical System.

If you are familiar with SingingBanana on youtube, he posted the following question: There is a 10 digit number where the first digit tells me how many 0 there are in the number, the second digit ...
0
votes
0answers
18 views

Transitive permutation groups & primitivity, 15-puzzle, Wilson

I'm reading the R. M. Wilson's paper about generalization of 15-puzzle to arbitrary graphs and I cannot understand the proof of following lemma: Lemma 3. Let $\Gamma$ be a transitive permutation ...
0
votes
1answer
103 views

Analogy between a Gödelian puzzle and Gödel's first incompleteness theorem

I'm studying Gödel's incompleteness theorems. And I have the following slide that defines a version of Gödel's first incompleteness theorem. The point is that one can always follow the math and get ...
-3
votes
1answer
507 views

Solve carefully [closed]

Solve carefully ... $$25-55+(85+65)=$$ You probably won't believe it, But this equals $5!$
0
votes
4answers
111 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.
11
votes
9answers
647 views

Make the number $100$ out of $1,2,3,$ and $4$ digits, without repeats

How can we make the number $100$, using only the following digits: $1,2,3,4$. You cannot repeat any of them.
0
votes
1answer
34 views

What is the likelihood of being killed by lightning in this situation?

There was a recent thunder storm in my city and it caused me to start thinking about a certain problem (perhaps it's my own, perhaps others have thought about it or some variant previously, I do not ...
0
votes
1answer
48 views

Choosing a number puzzle.

A and B play a game, where A begins the game. A can start the game by calling a number from 1 to 10, then the game continues by the other person choosing a number. But rule of game is if one picks x, ...
6
votes
3answers
344 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
69 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 ...
3
votes
2answers
683 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
67 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
266 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
69 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
135 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
85 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
110 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
50 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
113 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 ...
11
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
70 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
94 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
57 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
49 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
129 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). ...