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)

21
votes
0answers
424 views

The Right Triangle Game

I am looking for a deeper understanding, particularly the optimum strategy and the maximum score as a function of grid size, of the following (single-player) game played with an $n$ by $m$ grid: ($6 ...
16
votes
0answers
263 views

What Rubik's Twist configuration has the lowest visible surface area?

The Rubik's Twist has been a fun time sink. From the wiki page, [It] is a toy with twenty-four wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts, so that ...
6
votes
0answers
96 views

Fastest way to meet, without communication, in a toroidal palace?

I was interested by a similar question asked here, but wanted to pose a slightly different variant that avoids some of the pitfalls and ambiguities in the first question in order to ask something more ...
6
votes
0answers
240 views

History of a combinatoric problem: exchanging numbers by throwing stones

Another user recently asked a question on the Puzzling stack: Two spies throwing stones into a river. Suitably generalised, it becomes: Two spies (Alice and Bob) need to exchange a message. Each ...
6
votes
0answers
172 views

Card passing game, maximum length

Quoting from this question: There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two ...
5
votes
0answers
119 views

Puzzle - In how many pairings can 25 married couples dance when exactly 7 men dance with their own wives?

Each married couple as well as each dancing pair consists of a man and a woman. How many possible pairings are there? Here is the same question with a different amount of couples. I read the answers ...
5
votes
0answers
334 views

Cookie Clicker Chocolate Egg strategy

Introduction Cookie Clicker is a silly Javascript based web game. Here is a brief description of what you do: (description taken from this question: Explain a surprisingly simple optimization result) ...
5
votes
0answers
166 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 ...
5
votes
0answers
118 views

Find the number that follows the rules of two different series

I have this logic problem where I need to find a number that fits in 2 different series (vertical and horizontal). Each series has a rule, and once you find them, you can determine the answer. $$ ...
5
votes
0answers
337 views

A product puzzle

This is from a math contest. I have solved it, but I'm posting it on here because I think that it would be a good challange problem for precalculus courses. Also, it's kind of fun. Write the ...
4
votes
0answers
136 views

Is it a “paradox”, or a flaw in the question?

(Clearly not a pardox per-se but I would like to hear what you think) The basic riddle (not a very interesting one even) goes as follows: A first client comes into a barber shop, takes a hair cut ...
4
votes
0answers
140 views

How far away is that cloud?

A few weeks ago I was on an airplane and to pass the time started thinking about this problem. Using the following information, I wanted to know how far away a cloud I could see was. Under some ...
4
votes
0answers
120 views

Adding Numbers Pattern

A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
4
votes
0answers
105 views

A game on a smaller graph

In this question Alice and Bob play a game on $K_{2014}$, Alice directing one edge, Bob directing $1$ to $1000$ edges with Alice trying to make a cycle. The proof that Alice can win depended on the ...
4
votes
0answers
70 views

Would you please take a look if my substantiation is correct?

The four numbers 4, 5, 6, 7 are randomly inserted into 7 .3 .4 . 6 . 48 The result is a ten-digit number - for example, 7 4 3 5 4 6 6 7 48 How high is the chance, that the number created is ...
4
votes
0answers
207 views

Puzzle - zero knowledge proof

I am solving the following problem : I have edge-matching puzzles, where all pieces are squares and the grid has $n$*$n$ format. There is no global image to guide a puzzle solver. Despite the puzzles ...
4
votes
0answers
223 views

Can this be only solved by trial and error?

The following question was asked in a competitive exam Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the ...
3
votes
0answers
107 views

Worst case in decanting puzzles (pouring water from one jug to others).

A classic puzzle is to start with $3$ jugs of nonzero integer capacity ($A \ge B \ge C$) and have some water (integer) in each jug (the initial position). The goal is to get to some final (integer) ...
3
votes
0answers
31 views

Given $n$, find $a,b$ such that $a+b=n$ and $\Omega(a)+\Omega(b)$ is maximized

Given a number $n$, find $a,b$ such that: $a,b$ non-negative integers $a+b=n$ $\Omega(a)+\Omega(b)$ is maximized $\Omega(n)$ counts the number of prime factors of n (with multiplicity). ...
3
votes
0answers
200 views

Limits of infinite processes that terminate in finite time - checking my understanding?

I am a computer scientist by training, but have a fair amount of math background that I've picked up through classes, teaching, and general interest. A student of mine posed a question to me. I think ...
3
votes
0answers
79 views

Another machine problem

This is linked to my previous question Discounted optimization problem I have difficulties again finding a formula for $F(x)$. We consider a machine at time $t$ which is in state $x$. The machine ...
3
votes
0answers
143 views

placing coins on a table with a twist.

consider the classical puzzle, on a circular table, you and a friend take turns placing coins on the table and the first person who cannot do this loses. You can guarantee winning by placing the ...
3
votes
0answers
66 views

Calculating that confidence that pairs of lightbulbs are independently illuminated.

So, you're sitting in a dark room, and on the far wall you see $n$ lightbulbs mounted above plaques numbered $1$ through $n$. There is a lightswitch on the arm of your chair. Every time you flip the ...
3
votes
0answers
78 views

Question, need help finding the source.

I was hoping someone could tell me if they knew the source to this problem: Let S be a subset of {1, 2, 3, 4,..., 10, 11}. We say that S is LUCKY if no two elements of S differ by 4 or 7. The ...
3
votes
0answers
643 views

Four candle problem: Using candles as timers

The candles each take one hour to burn completely. Cutting off bits of the candles is forbidden, but the candles are placed on a raft of fork handles so they may be burnt at both ends (e.g. to time ...
3
votes
0answers
103 views

Least characters in a numerical representation of integers

I was wondering what the shortest way to represent any given number is. For example, $387420489=9^9$. So, for this case, the smallest representation is of order 2 (2 numbers). Alternatively, ...
2
votes
0answers
55 views

A fashion victim puzzle

Consider $n \in \mathbb{N}$ fashion-sensitive kids, each wearing a T-shirt; for simplicity, kid $i \in \{1, \ldots, n\}$ initially wears shirt $i$. Tastes over the shirts are summarized in an $n ...
2
votes
0answers
33 views

Symbolically formulate the two guard problem so it can be solved by a computer

Take the classic two guard riddle (I don't know where the origin of this riddle is, so I'll take the version from http://www.calpoly.edu/~mcarlton/riddles.html): You stand at a fork in the road. ...
2
votes
0answers
89 views

Math puzzle I have been stuck on

Have had this math puzzle that I have been unable to solve for a while. Each leter is a number between 1-9. No letter uses the same number twice (aka if B is 3 D can't be 3 also). The ? mark ...
2
votes
0answers
90 views

ZELDA Guardian Puzzle Part II - Shortest Path (Unsolved for new rules)

This question is in relation to the following previously asked question: Twilight Zelda Guardian Puzzle : Shortest Path (UPDATE: ADDED RULES) A 1-step-less solution was uncovered, but under an ...
2
votes
0answers
51 views

The $8$-Puzzle and $2$-Cycles

I have been studying the $8$-puzzle and have thus far managed to wrap my head around the following information: The following illustrates the solved position of the $8$-puzzle, where $9$ is the empty ...
2
votes
0answers
260 views

How to solve instant insanity puzzle with graphs.

So I have a 10 cube insanity puzzle, I constructed the graph (I'll post pc later) based on the colors the problem is that there is just way to many lines and nodes to see the solution. Is there any ...
2
votes
0answers
102 views

A river crossing puzzle with relatively prime problem

I want to share a problem on a facebook group : https://www.facebook.com/groups/419858384791916/permalink/640398286071257/ 99 people, numbered 2 to 100, are all on one side of a river and wish to ...
2
votes
0answers
83 views

How can this paradox be resolved?

I came up with a (probably unoriginal) paradox today, and was wondering how it might be resolved. Its approach to reasoning seems to resemble basic game theory techniques. Suppose a casino game has ...
2
votes
0answers
44 views

determine the number thought of

Ten people are seated around a circular table. Each of the ten people thinks of a number and whispers it to his/her two neighbours. Then these ten people announce the average of the two numbers they ...
2
votes
0answers
52 views

Number of tries to guess M-1 letters from M-letters-code.

There are N letters in an alphabet. There is a combination lock, the code to it consists from M different letters. You can input M letters combination to try to open the lock. If you guess at least ...
2
votes
0answers
61 views

R. Jeffrey and the Three Prisoners

Here’s something curious, from p. 26 of the estimable Richard Jeffrey’s last, posthumously-published book, Subjective Probability: The correct (or at least orthodox) answer to this puzzle would be ...
2
votes
0answers
109 views

A mathematical game: moving tiles

There is a mathematical game called moving tiles. There are $8$ different movable tiles on a $3 \times 3$ board, At the beginning the tiles' location is given as following: ...
2
votes
0answers
460 views

What is the highest possible score in 2048 hard?

There is a variant of the popular game 2048, called 2048 hard or 2048 impossible, which automatically places each new tile in the hardest possible location. Is this variation possible to solve, and if ...
2
votes
0answers
322 views

Number of paths in a grid

A common puzzle problem is to count the number of paths that start from the bottom-left-hand corner of a grid and end at the top-right hand corner, with the restriction that you can only move upwards ...
2
votes
0answers
81 views

Math Puzzle, finding a sequence with a certain property

A certain number of the $5000$ members of the Conway Mathematical Society (each of which has a different membership number between $1$ and $5000$) got together to discuss a puzzle. Much to their ...
2
votes
0answers
365 views

Given a number of items, how many sets of three are there where no two sets are two thirds similar?

Sorry if the title isn't proper math-talk. Hopefully I can explain it better here. So let's say we have a set. 1, 2, 3, 4, 5, 6, 7, 8, 9. I want to know how many groups of three can be made where no ...
2
votes
0answers
89 views

Minimum Overlap

You have a set of ten numbers, and you are trying to cover all 4-element subsets of this set. To do this, you choose 5 elements from the set every time and you cover all 4-element subsets of your ...
2
votes
0answers
59 views

Visually apealing holologous transformation of a given contour

There is this problem which roughly says: You want to put a framed picture onto the wall with a cord to the picture frame. The cord is a single one, and both ends are attached to the frame. ...
2
votes
0answers
173 views

Make one cube out of 8 little cubes

As part of a puzzle, you have to stack 8 little $1\times 1\times 1$-cubes so that they form one big $2\times 2\times 2$-cube. Now I want to check all possible solution to the puzzle and therefor I'm ...
2
votes
0answers
112 views

Can 24 lines on a cubic surface be realized as 24 identical spiral rods?

It's possible to put 24 lines on a cubic surface. 27 lines is possible, but I don't have a great picture for that surface. It turns out that the 24 lines can be built with Zome. I'm thinking that ...
1
vote
0answers
35 views

Guess the rule of transformation of a natural number

I came across a playful problem. On a sheet of paper it is written the number $\overline{1234xy}$, where \begin{equation}\overline{1234xy}=1*10^5+2*10^4+3*10^3+4*10^2+x*10^1+y\end{equation} Five ...
1
vote
0answers
43 views

A harder long division puzzle than the first; what should “Algebra I” solution look like?

Here's another problem, significantly harder than the first, but still accessible to target audience. The statement of the problem (i.e., northwest corner only) comes from a PennyDell puzzle magazine: ...
1
vote
0answers
117 views

The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain?

The question in the textbook is: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much a day does the clock gain? My method: The correct ...