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

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An interesting way to visualize the Mandelbrot Set. Proofs? Simplifications? Extensions?

This is a multi-part Question. Please chime in with any interesting insights in addition to Answers. I have noticed some interesting properties of Mandelbrot series that lead to a different way to ...
3
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30 views

Hamiltonian path on a chessboard with prescribed endpoints

On an 8 x 8 chessboard consider two squares to be adjacent if and only if they share a common side. All paths below will consist of steps which join one square to an adjacent one. Under these ...
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39 views

Fun Q2: Polygon inside a polygon. Find Test's area.

A triangle is drawn of side length $a$. Then a square is drawn inside the triangle such that the area of the square is maximum and the bottom side is shared. Then a regular pentagon is drawn inside ...
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39 views

minimum number of times to change tyres.

I saw this brain teaser. Suppose, we travel 1000 miles on a tricycle and we have 5 tyres, then how many times do we need to stop to change tyres so that each of the tyres travelled the same ...
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184 views

The mathematics of a drinking game called Spoon

This question is about the drinking game Spoon. It was asked on reddit.com/r/math : http://www.reddit.com/r/math/comments/3i9790/drinking_game_turned_mathematical/ The question is whether the person ...
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101 views

Trajectories on a circular billiards table

This question is related to The case of Captain America's shield: a variation of Alhazen's Billard problem, but more focused. Let the unit disc in the plane be our billiards table, and let $C$ ...
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88 views

Is this proof of a mathematical olympiad problem correct?

I'm quite sure about the exactness of my proof, but I'd like to hear (constructive) criticism about my writing. This is the problem: Every non-negative integer is coloured white or red, so that: 1) ...
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82 views

Bitcoin math problem example

Disclaimer: I'm not a mathematician, if something is complicated, please use layman's terms. Thank you. I'm wondering about this bitcoin thing. I have heard that mining is using a computer to solve ...
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95 views

Josephus Variant

I set myself the challenge of trying to solve a variant of trying to solve a variant of the josephus problem where instead of killing every second person, every third person dies. The formula for the ...
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205 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 ...
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202 views

Prime factor of $14 \uparrow \uparrow 3 + 15\uparrow \uparrow 3$ wanted

Checking the prime factors of the numbers $$z(a,b) \ := a \uparrow \uparrow 3 \ +\ b \uparrow \uparrow 3 \ ,$$ a,b positive integers with a < b the number $$z(14,15) = 14 \uparrow \uparrow ...
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225 views

Help explain why (or why not) the solution for a in $\sum_{n=1}^\infty (-1)^n\times(n^{1/n}-a)=0$ is 1-2$C$MRB

$C$MRB is approximately 0.1878596424620671202485179340542732. See this and this. $\sum_{n=1}^\infty (-1)^n\times(n^{1/n}-a)$ is formally convergent only when $a =1$. However, if you extend the ...
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470 views

Guilloché security printing — can it be cracked?

Money uses Security printing, and often uses Guilloché patterns. These curves are inscribed by wheels on wheels on wheels, ten wheels deep in some cases. For example, the back of the US $1 bill has ...
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117 views

A photon in expanding Universe (a snail on a tree)

I want to know how far a snail can reach in expanding universe. It has a constant speed c = 1 and tree is expanding at speed $v= H_0 D$, with Hubble constant $H_0 = 1$. Here D(T) is the distance of ...
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46 views

How to find the point in a closed geometrical figure which maximizes the “direct-line-of-sight function”

To expand upon the title, and put it in clear terms, I phrase the problem thusly: Consider the interior of any continuous, closed, non-self-intersecting curve in the plane. (I'm not sure if I'm ...
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892 views

Turning radius of a vehicle

What's the minimum turning radius of a vehicle, rectangular in shape, with length l units and width w units? One key point to consider, would be that, the inclination of the front wheels can be ...
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157 views

Is there a way to determine how many solution does “ The hundred Fowls problems” have looking at the coefficients?

I was looking at the different versions of the hundred fowls problems. I came across the problem posed by Chinese mathematicians posed in 5th century,and then Indians in 9th, 10th centuries. Alcuin of ...
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154 views

For which positive integers n does there exist a prime whose digits sum to n?

Motivated by this earlier question, I thought of this problem: Question: For which positive integers $n$ does there exist a prime whose decimal digits sum to $n$? We can make two "easy" ...
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402 views

“Green Globs” question

When I was in high school geometry, we had a fun little game on the computer called Green Globs (the website for the software is http://www.greenglobs.net/index.html). A number of targets (globs) are ...
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672 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 ...
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106 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, ...
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95 views

How to find Misiurewicz Points without solving huge polynomials? (Mandelbrot Set)

Here is a plot of 17,723 Misiurewicz Points. The code below generates a set of polynomials u[m,n], the roots of which have periodicity (m-n) starting at iteration n. I stopped at 17,723 points ...
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37 views

The hardest game of mahjongg

I was playing Mahjongg solitaire the other day. It got me thinking... The board has $2n$ pieces at the beginning and assuming that the game is winnable. The game would be trivial if there would be ...
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65 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 ...
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116 views

How can all players in the Starcraft 2 Grandmaster league win more than they lose?

Starcraft 2 is a competitive online strategy game where players compete in leagues with other players of similar skill. The most difficult and highest league is the Grandmaster (GM) league, which ...
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60 views

Compute shooting targets for the gunmen

This is an extension of the well known "3 gunmen puzzle": N gunmen with hitting probabilities in (0,1] take turns to shoot at each other. Firing order is fixed (gunman 1 shoots first, then gunman ...
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55 views

Could you suggest books, papers or problems that could be used as good “general” motivating examples of calculus application?

I would like to stress the kind of reference I am looking for... In statistics there are lots of motivating (and sometimes unexpected) examples that are interested for everyone such as Birthday ...
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70 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 ...
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44 views

Queen moves — The Squared Chain Puzzle

Karl Scherer made the interesting Squared Chain Puzzle. Start with a $7\times7$ board, with a queen somewhere. Make a legal move with the queen, placing coins over all squares visited. For subsequent ...
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32 views

Alternative Arithmetics

In Anderson et. al 2010, "Cognitive and metacognitive activity in mathematical problem solving: prefrontal and parietal patterns", the experimenters taught people how to solve a novel system of ...
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49 views

Rifleman game with $n$ players in $D$ dimensions: what is the survivor fraction when $n,D\to\infty$?

This is a follow up to this question where the following problem is explored (for $D=2$): $n$ riflemen are distributed at random points in $[0,1]^D$. At a signal, each one shoots at and kills his ...
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66 views

Is there a contiguous locus of the equality $a = b$ in $\zeta(\rho + \varepsilon)=a + î b$ in the near of a root?

This is just by an accidental couriosity: In the near of a root $\rho$ of the Riemann's zeta - can there be a continuous line starting from $\zeta(\rho)=0$ to $\zeta(\rho + \varepsilon_j)=a_j + î b_j ...
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61 views

Start with a circular cake…

This is a random math question I saw and it piqued my interest. I like cake. Start with a circular cake and cut it with five straight slices. What is the largest number of pieces that you can create ...
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26 views

Help with understanding Rating Systems

Hey guys so I'm trying to come with a rating system from 1-10 that will be determined based on how close a user is to an average value that I have. I don't have any data(other than the average value) ...
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51 views

Puzzle about decomposing numbers with $+, -,\times, \div$

In the book The Moscow Puzzles by Kordemsky I came across the following puzzle (no. 47): Express 100 three ways with five 5s. You can use brackets, parentheses, and these signs: $+, -,\times, ...
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100 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 ...
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46 views

The odyssey of spies: Kryptos

The part four $K4$ of Sanborn sculpture, a sculpture located on the grounds of the CIA in Langley remains unsolved. As you can read in [1], Sanborn released a clue for the 64th-69th letters in part ...
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78 views

Efficient elevator strategy

Suppose an institution building has 12 floors and there are a total of 8 lifts. Now lets say a situation arises at peak times where almost all the lifts are crowded and people randomly enter any lift, ...
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40 views

making integers from a given set

this Q is very easily generalizable. For example consider $1,2,3$ and $4$. We have $1=1, 2=2, 3=3, 4=4, 5=4+1, 6=2\times 3, 11=4\times 3-1$. You can only use each number once. 37 is the first number ...
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21 views

Find least numerator and denominator for a given sequence of numbers in decimal form

Say I have a sequence (s) of digits written as number. (Ex: 1234567890) I need to find out shortest possible pair of numerator (n) and denominator (d) that ,being converted to decimal form of fraction ...
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42 views

Can i connect these points in a way that satisfies these conditions?

I apologise in advance for the horrible phrasing. If you imagine 3 points like this: You would then draw a path between A and B and another between B and C, such that the length of the line AB is ...
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47 views

How to maximize the minimal amount not payable with the exchange of at most two coins?

Background I've been thinking about payments which you can do using at most two coins. This includes three possible cases: You pay by giving one coin of the value you owe (for example, if you have ...
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76 views

Does typesetting of mathematical content differ in right-to-left languages?

Languages such as Arabic or Hebrew are written right-to-left. Does the way mathematical content is written differ in those languages? Some simple examples of which I would be interested to know how ...
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111 views

What is the best way to master my algebra skills without taking an algebra class?

I was in advanced math my entire life. I got through all the math I needed for my original degree. 8 years later here I am changing degrees and I need more math. I just took calculus I and I passed ...
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63 views

Placing $4n$ non-attaking queens of in a $4n \times 4n$ chessboard.

Is it possible to place $4n$ non-attaking queens of in a $4n \times 4n$ chessboard?? I have found that it can be done for $4 \times 4$ chess board and trying to extend it to $8 \times 8$ chessboard ...
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47 views

Is there an intuitive reason why hippopede, the intersection curve of a sphere and a cylinder, is traced by composing two rotational motions?

The hippopede is historically famous because Eudoxus used its properties in the first mathematical model of planetary motion. He nested concentric spheres rotating at different inclinations to each ...
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87 views

area estimation with tiling

For any given shape drawn on a graph paper, a kid can calculate the area of any shape by counting the tiles with a simple formula: any edge covering 50% or more, mark the tile; total area = sum all ...
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60 views

Shannon number upper and lower bounds

What are the best proved upper and lower bounds for the Shannon number, i.e. number of possible positions of chess? Is the upper bound 7728772977965919677164873487685453137329736522 given in ...
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606 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 ...
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92 views

How much advantage would a Blackjack player gain by being able to see the underside of cards?

In the novel Spaceland by Rudy Rucker, the protagonist Joe Cube is grafted with an eyestalk that sticks vout into the fourth dimension. This lets him see under and inside three-dimensional objects ...