# Tagged Questions

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

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### Number of combinations of $k$ numbers using arithmetic operations

What is the maximum number of positive rational values that can be obtained by combining $k$ positive integers using only addition, subtraction, multiplication, division, and parentheses? Assume that ...
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### How to mathematically color the regions bounded by a parametric curve?

Usually, if an implicit equation F(x,y) = 0 defines a curve (or curves) on the x-y plane, then we can use the inequalities F(x,y) < 0 or F(x,y) > 0 to color the regions bounded by the curve (or ...
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### How to tell if a Rubik's cube is solvable

How can I determine if a certain Rubik's cube, that is in a certain state, is solveable? By "certain state" it could mean that the cube has been dismantled and put together again. And in my experience ...
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### Is Mega Millions Positive Expected Value?

Given the rapid rise of the Mega Millions jackpot in the US (now advertised at \$640 million and equivalent to a "cash" prize of about \$448 million), I was wondering if there was ever a point at ...
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### Largest $x$ such that the power tower (tetration) $x^{x^{x^{x^{…}}}}$ converges? [duplicate]

Possible Duplicate: Infinite tetration, convergence radius Recently in this thread, Pseudo Proofs that are intuitively reasonable, I learned that ...
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### $3 \times 3$ Magic Square of Squares

On picture below is three-by-three magic square in which seven of the entries are squared integers, found by Andrew Bremner of Arizona State University (and independently by Lee Sallows of the ...
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### How to estimate the number of articles on Wikipedia using the “random article” function?

There is a Wikipedia-type website of a fixed size of $S$ number of articles. You start at any article on Wikipedia. You then start to press the "random article" button and count the number of times ...
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### Geometrical combinatorics

This question was inspired by Rush Hour game: You have a 6x6 grid, 12 pieces of size 2, and 4 pieces of size 3. A piece can be placed on the grid either horizontally or vertically. The pieces can't ...
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### Combinations of a penny, nickle, dime, and quarter

You have one penny, one nickle, one dime, and one quarter. How many different amounts of money can you make using one or more of these coins? Please help me! I'm having trouble! Im having trouble I ...
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### Mathematics From Futurama

Dear Professor Farnsworth, We at D.O.O.P are trying to mathematically model a rocket ship fueled by your employee Leela's pet Nibbler's pooped Black matter. Obviously this rocket ship is fueled by ...
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### Calculating Gröbner basis for Sudoku

I'm trying to write a program that solves sudokus using a Gröbner basis. I introduced 81 variables $x_1$ to $x_{81}$, this is a linearisation of the sudoku board. The space of valid sudokus is ...
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### What is the probability that a solitaire game be winnable?

By "solitaire", let us mean Klondike solitaire of the form "Draw 3 cards, Re-Deal infinite". What is the probability that a solitaire game be winnable? Or equivalently, what is the number of ...
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### Find the angle between two lines using a compass and straight edge.

I've drawn two random, non-parallel, straight lines on a plane. They cross over, forming two angles, a and b, where (a + b + a + b) = 1 (or 360°) and a ≤ b. (Making a either the acute angle or a right ...
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A riddle was posted in this mathoverflow question: http://mathoverflow.net/questions/85439/how-does-intuitionism-handle-this-riddle A riddle: You and another person are kidnapped and knocked ...
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### A binet-like formula for $\small 1 , 2 , 3 , 6 , 9 , 18 , 27, 54, 81, \ldots$?

This is more a "recreational" problem. By another question I came to the question for a closed-form-formula for this sequence $\small 1 , 2 , 3 , 6 , 9 , 18 , 27, \ldots$ which is just the mixture of ...
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### Number of knots possible with length L string

What is the asymptotic growth in L for the numer of topological different knots possible using a length L closed string of radius 1? In 3 dimension euclidean space.
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### 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 ...
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### 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 ...
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### 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 ...
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### Math and Logic of Infinite Chess

Hello could you help me in this... Two players (White and Black) are playing on an infinite chess board (extending infinitely in all directions). First, White places a certain number of queens (and ...
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### 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 ...
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### 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? ...
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### Proving you *can't* make $2011$ out of $1,2,3,4$: nice twist on the usual

An undergraduate was telling me about a puzzle he'd found: the idea was to make $2011$ out of the numbers $1, 2, 3, 4, \ldots, n$ with the following rules/constraints: the numbers must stay in order, ...
10k views

### Probability of winning a prize in a raffle

My work is having it's annual Christmas raffle today. 1600 tickets have been sold, and there are 40 prizes to win. I have bought ten tickets. What are the odds I will win a prize? While an initial ...
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### What's the largest possible volume of a taco, and how do I make one that big?

Let $f$ be a continuous, even, positive function over some interval $I=[-a,a]$ such that the total arc length of $f$ over $I$ is at least $2$, $f(0)=0$, and $f$ is increasing on $(0,a)$. View the ...