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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-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?
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 ...
3
votes
2answers
147 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 ...
2
votes
1answer
46 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
506 views

Solve carefully [closed]

Solve carefully ... $$25-55+(85+65)=$$ You probably won't believe it, But this equals $5!$
2
votes
0answers
132 views

Number of ways to color a grid?

I have a $N \times M $ grid and I am trying to calculate the number of ways I can color this grid in maximum $k$ colors (I can use only $2$ colors or all $k$ colors) with the exception that two ...
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, ...
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 ...
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
1answer
65 views

Did the U.S. Army use a formula to evaluate fitness performance?

While writing a web app to calculate one's score on the Army Physical Fitness Test (APFT), I grew tired of simply retyping this chart: ...
1
vote
2answers
65 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 ...
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 ...
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 $\infty$ ...
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 ...
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 ...
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 ...
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 ...
3
votes
0answers
83 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
109 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
49 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
112 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 ...
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
56 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
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
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
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 ...
0
votes
0answers
40 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 ...
1
vote
2answers
166 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
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) ...
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
38 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 ...
2
votes
0answers
94 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 ...
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 $n$, ...
1
vote
3answers
195 views

Bucket Puzzle Probability Problem

You have 2 buckets. One full of white marbles and the other full of black marbles (equal amounts). How do you allocate the marbles into two buckets in a way that maximizes your probability of picking ...
1
vote
1answer
92 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
204 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.
2
votes
1answer
240 views

Find distance between two figures

I was trying on this problem. All information is in picture. The aim is to find $AB$. It looks very simple problem. I spent more than one hour to solve it but I can't. It looks simple,but equation ...
0
votes
0answers
26 views

How many digits of an $n$ digit positive integer do I need to know to correctly guess the first $m$ digits of the $k$ th root of $n$.

Please help me solve this puzzle, which in my opinion only sounds tough: How many digits (counting from the left) of an $n$ digit positive integer do I need to know to correctly guess the first $m$ ...
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 ...
1
vote
1answer
31 views

Is every nonogram an erased version of a slightly fuller nonogram?

Say we have an $N\times M$ binary nonogram, where the $i^{th}$ row has to sum to $n_i$, and the $i^{th}$ column has to sum to $m_i,$ so that we have constraints $(n_1,\dots,n_N)$ for rows and ...
3
votes
3answers
134 views

Does there exist $n$ such that all numbers $n,2n,\dots,2000n$ have the same digits?

Does there exist a number $n$ such that all numbers $n, 2n, 3n, 4n, \dots, 2000n$ have the same multi-sets of digits except zeroes? (Having the same multi-sets of digits excepts zeroes means ...