Questions tagged [recreational-mathematics]

Puzzles, curiosities, brain teasers and other mathematics done "just for fun".

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7
votes
4answers
541 views

How many ways can we place these ships on this board?

I want to find out how many ways we can arrange these ships on this field. I just have no idea how to go about solving this. So I bring it to the Pros! The board is an 8 by 8 Board. There are 5 ...
-1
votes
3answers
157 views

From a mathematical point of view is it optimal in no limit texas hold em to play with more money than less?

I noticed the other time a friend of mine went to a casino and bought in 100 dollars for a 1-2 table. Other players had heavier buy ins. I have received two opposing arguments. One says that buying in ...
3
votes
1answer
191 views

Optimal polyomino induced coloring

Which polyominos (with orientation) of $n$ squares, requires the least number of different colors, $c(n)$, such that if this polyomino is placed anywhere on an optimally colored infinite square grid ...
14
votes
5answers
19k views

How many bananas can a camel deliver without eating them all?

This is a fun puzzle I was assigned on the first day of highschool (over a decade ago). I just dug it up randomly from under my bed and thought I'd share it with the SE community. At the time, I ...
22
votes
4answers
2k views

Something that I found, and would like to see if it's known.

Well I am quite sure it's known (I mean number theory exists thousands of years), warning beforehand, it may look like numerology, but I try not to go to mysticism. So I was in a bus, and from ...
3
votes
0answers
955 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 $1/...
1
vote
0answers
118 views

Boggle dice set letter distribution algorithm [duplicate]

Possible Duplicate: Boggle letter probability What algorithm have the creators of the word game Boggle used to come up with these dice sets? ...
0
votes
1answer
875 views

Roulette betting options

I'm learning binomial distributions and I came across this problem: Let r.v X be winning from a bet on a split in roulette and Y be be winnings from a bet on red color. X = 17 (2/38 chance) and -1 (...
6
votes
1answer
383 views

How many states in the game of hex?

I am trying to calculate how many unique states are possible to be in during a game of hex. The upper bound for an $n\times n$ board is $3^{n^2}$. This is ignoring gameplay and simply considering ...
5
votes
1answer
543 views

Is there an analytical solution to this nonlinear ODE?

Is there an analytical solution to the nonlinear ODE $$\frac{dx}{d\theta} = -\sqrt{\frac{x^2}{4\cos^2\theta} - \cos^2\theta}$$ over $\theta \in [0, \pi/2]$ with initial condition $x(0) = 2$? Using the ...
5
votes
2answers
2k views

Is this version of the Hanoi towers problem NP-complete?

This was really inspired by Solitaire, but a few people reacted with ``oh, it's like the towers of Hanoi, isn't it?'' so I'll try to pose the problem in terms of discs here. Let's start. There are n ...
17
votes
2answers
603 views

Who has the upper hand in a generalized game of Risk?

So, I played a game of Risk the other day for the first time since I was very little. I was frustrated to discover that I couldn't compute (at least not in my head) whether the attacker or the ...
0
votes
1answer
82 views

Probability, why my solution doesn't work out? (P of drawing a pair)

The task is simple, the probability of drawing a pair of cards. You draw two cards from a stack, what is the chance that you get two kings or two fours. My idea was the following. There are 13 ...
3
votes
2answers
16k views

Solving an inequality, the equality is facing the wrong way?

I'm suppose to solve a problem that goes like this. The graph for the following function f given by $f(x) = 115.82 \cdot 0.94^x + 5$, with $x \geq 5$, gives the temperature of the water after it's ...
3
votes
4answers
1k views

Is there an algorithm to recover a crossword grid based on the clues alone?

Suppose that we have access to only the clues of a crossword puzzle along with the number of letters that the answers are supposed to be. Is there an algorithm that we can use to reconstruct the ...
3
votes
0answers
125 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, $10=2\...
0
votes
1answer
57 views

Drawing three cards of different type

I did draw a tree and found out that this can be done in 24 different ways. But is there a quicker formula? There are a total of four different types of cards, as you know. And we are to draw three of ...
4
votes
2answers
462 views

Counting ordered triples of non-negative integers not greater than 100

Can we find the number of ordered triples $(x,y,z)$ of non-negative integers satisfying (i) $x \leq y \leq z$ (ii) $x + y + z \leq 100$? Source:Regional Mathematics Olympiad India (2003) Thank you.I ...
7
votes
2answers
676 views

Solving math word problems WITHOUT brute force

How can we solve these problems withing using brute force? http://edhelper.com/math/multiplication51.htm
20
votes
1answer
570 views

Extracting individual race results from Mario Kart final scores

In Mario Kart, one "cup" involves 4 races, and after every race each racer gets points awarded based on what place they came in (better rank means more points). After playing it enough I grew curious ...
5
votes
2answers
841 views

Famous Finite Sets [closed]

What are the most famous (or most beautiful, IYO) finite sets in mathematics? I'm especially looking for 'large' sets that contain more than $2^{10} \approx 1000$ but fewer than $2^{20} \approx 1{,}...
6
votes
1answer
852 views

Decomposing a circle into similar pieces

Is it possible to decompose a circle into finitely many similar disjoint pieces, one of which contains the circle's center in its interior?
17
votes
2answers
1k views

Minimally inconsistent Sudoku puzzle

A sudoku puzzle is a partially filled $9\times 9$ grid with numbers $1,\ldots,9$ such that each column, each row, and each of the nine 3×3 sub-grids that compose the grid does not contain two of the ...
3
votes
2answers
1k views

In Towers of Hanoi (with 3 sticks and n disks without backtracking), do all legal sequences of moves reach the solution?

Updated Question : How to show that in TH we never reach a state where there are no paths to the solution? ( without reversing moves, as if reversing is allowed this becomes trivial ) Edit : Thanks ...
18
votes
4answers
2k views

Fun math for young, bored kids?

For 6 months, I'll be organizing, as part as my volunteer work in an NGO, math classes with small groups (~10 students, aged 16 or 17). These classes are not compulsory, but students willing to stay ...
8
votes
1answer
1k views

Solving $n$-queens with determinants

I keep reading about a proposed method of finding solutions to the $n$-queens problem using determinants, but I can't find any specific details anywhere. Can somebody explain to me how to find ...
10
votes
2answers
350 views

Zombie Survival: What is the optimal way to place seven entities on an infinite grid to reduce number of adjacent pairs?

I am designing a zombie-survival type scenario in a tabletop RPG game. My system is going to work in such a way that the players take damage at the start of their turns based on how many adjacent ...
4
votes
2answers
1k views

Minimal number of solutions to a sudoku cube

A "Sudoku cube" is a 3x3x3 uncoloured Rubik's cube. In the solved state, each face has the digits 1 through 9 arranged in ascending rows from top to bottom, and all of the digits on a given face have ...
0
votes
3answers
2k views

Triangle whose height and sides are consecutive integers

This is probably a old puzzle,and maybe you have seen it somewhere else before.Imagine a special triangle. The height and the three sides of this triangle are 4 consecutive integers.Can you figure out ...
6
votes
1answer
411 views

Expressing any given number in the form of $x^y + y^x$

I was told by one of my friends that any given positive integer can be expressed in the form of $x^y + y^x$ where x & y are integers. For example: 17 = $2^3+3^2$ Surprisingly,this could be done ...
28
votes
1answer
2k views

Expert Minesweeper Probability Question

This is just a question I thought of while playing minesweeper. I think that finding the solution might be kind of fun, so I'm sharing it with you guys. If you have no concept of what minesweeper is, ...
1
vote
4answers
477 views

Proof for divisibility rule for palindromic integers

I am studying for a test and came across this in my practice materials. I can prove it simply for some individual cases, but I don't know where to start to prove the full statement. Can you help me? ...
3
votes
2answers
217 views

Five Fridays and Sundays on October

How to prove that if you take any 400 consecutive Octobers then exactly 14 % of those years have five Fridays and Sundays?
1
vote
1answer
137 views

Need help on proceding a paper about estimating numbers of sudoku

I was reading a paper that I found via spiked math (http://spikedmath.com/comics/424-the-numbers-quiz-solutions.png): http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf. I have problem ...
2
votes
1answer
782 views

The Game of Nim

A position in Nim consists of some piles of coins. Two players alternate, with each move removing a portion of one pile. The winner is the player who takes the last coin. Suppose that the starting ...
5
votes
2answers
568 views

Finding the largest set of integers over an interval where the sum of any 'k' elements is unique

Consider the set $(s_1, ..., s_N) \in S$, where all $s_i$ are positive integers selected from some interval $[M, L]$ and the sum of any $k$ integers in $S$ is required to be unique and to have a ...
4
votes
1answer
363 views

The “beach problem”: does anyone know it? or know how to solve it?

The following problem was given some years ago in the German computer-science contest for pupils ("Bundeswettbewerb Informatik"). It was originally wrapped in a story which I will briefly translate ...
1
vote
3answers
166 views

compare which two cube is the same

I am solving following problem: The problem states that on figure 1 there is shown a cube with three facets on which there is drawn three section(length). This cube was put on other facet and ...
2
votes
1answer
104 views

How determine largest reflected number

I was trying to determine maximum number from list of given integer in problem 8 here (page 5). So as you see, there are 5 written numbers on paper, and on the wall there is a hanging mirror. We ...
0
votes
3answers
265 views

Deconstructing $0^0$ [duplicate]

Possible Duplicate: Zero to zero power It is well known that $0^0$ is an indeterminate form. One way to see that is noticing that $$\lim_{x\to0^+}\;0^x = 0\quad,$$ yet, $$\lim_{x\to0}\;x^0 = ...
2
votes
3answers
363 views

Squares on a checkerboard

How many squares of all sizes arise using an $n$-by-$n$ checkerboard? How many triangles of all sizes arise using a triangular grid with sides of length $n$ ?
0
votes
1answer
94 views

Game statistics: Extracting interesting patterns out of users and level

I made a small game and in course of time collected fair amount of data between users and level The level chart is long (120 levels) but looks somewhat like this $$ \begin{array}{|c|c|} \text{...
2
votes
1answer
213 views

Evenly dividing candy bar into $n$ pieces

I have 2 friends. We have one candybar and we want to divide it evenly. Unfortunately we don't have any way of accurately measuring and cutting the candybar. Therefore we are looking for a method ...
18
votes
1answer
689 views

Choosing points in fractions of the unit interval

How long a series of points in (0,1) can be chosen such that the first two are in different halves, the first three are in different thirds, ... the first $n$ are in different $n^{\text{th}}$s? My ...
6
votes
2answers
206 views

Why are the periods of these permutations often 1560?

I ran across a math puzzle that went like this: Consider the list $1,9,9,3, \cdots$ where the next entry is equal to the sum mod 10 of the prior 4. So the list begins $1,9,9,3,2,3,7,\cdots$. Will ...
5
votes
2answers
158 views

Avoiding matching first digit of $a^n$ with $b^n$

For any given pairs of positive integers $a$ and $b$, is it possible that the first digit of $a^n$ never matches the first digit of $b^n$ for any positive integer $n$? (If $a=2$ and $b=5$ the only ...
9
votes
1answer
343 views

Cube skeleton bindings

Imagine that you have a cube skeleton, like so: Further imagine that you have three rubber bands that you can loop through any of the faces. However, only one rubber band may go through any ...
3
votes
2answers
1k views

Decryption Problem

The following message was posted in our math department and I wouldn't mind some help into getting started at cracking it: gectl atnoy danwm etaim oroni snair ohass wveno faome nceto kils Any ...
2
votes
0answers
211 views

$n$ by $n$ Primally Magic Squares

(Again copied verbatim from a September 2009 thread I made.) A Primally Magic Square (PMS) is exactly like a traditional magic square with a change of criteria. Where a traditional magic square is ...
6
votes
1answer
1k views

How many steps does it take the computer to solve a Sudoku puzzle?

We all know what Sudoku is. Given a Sudoku puzzle, one can use a simple recursive procedure to solve it using a computer. Before describing the algorithm, we make some definitions. A partial solution ...