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

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0
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1answer
51 views

Ramsey's Theory and Tic-Tac-Toe analogy.

I read, briefly, about a connection between Ramsey's Theory and Tic-Tac-Toe. From my understanding, it went like this: Imagine playing Tic-Tac-Toe in a k-dimensional hyper-cube. There is such a ...
0
votes
1answer
100 views

How to solve simple programming problem with strange math question?

Here is the question: A cookie recipe calls for the following ingredients: 1.5 cups of sugar 1 cup of butter 2.75 cups of flour The recipe produces 48 cookies with this amount ...
1
vote
1answer
68 views

What is the shortest LOOP program that outputs 2016? [closed]

Use a minor restriction of the LOOP language described under Wikipedia's "LOOP (Programming Language)". The restriction is to eliminate constants. So, the language contains increment: $x_i++$, ...
0
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0answers
21 views

Solving Trigon Puzzles

The Trigon puzzle consists of a grid of triangles arranged in shapes with both outside borders and "holes" in the center. Each triangle has a sum between 0 and 18. The goal is to assign values to ...
0
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1answer
160 views

A function f(n) satisfies the recurrence f(n)=4f(n/2)+n for real numbers. Give an upper bound for f(n)?

A function f(n) satisfies the recurrence f(n)=4*f(n/2)+n for real numbers. Give an upper bound for f(n)? I get somewhere T(n) = Θ(n^2), is that correct?
11
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0answers
552 views

Any other Caltrops?

This question has been edited. The regular tetrahedron is a caltrop. When it lands on a face, one vertex points straight up, ready to jab the foot of anyone stepping on it. Define a caltrop as a ...
1
vote
1answer
29 views

Reflected rays bouncing in a regular polygon?

Suppose we have the following scenario: You are standing in a room that is in the shape of a regular n sided polygon with mirrors for walls. You shine a light, a single ray of light, in a random ...
2
votes
0answers
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 ...
2
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1answer
31 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
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0answers
17 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 ...
21
votes
1answer
553 views

Is this a way to prove there are infinitely many primes?

Someone gave me the following fun proof of the fact there are infinitely many primes. I wonder if this is valid, if it should be formalized more or if there is a falsehood in this proof that has to do ...
14
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3answers
218 views

Finding the common integer solutions to $a + b = c \cdot d$ and $a \cdot b = c + d$

I find nice that $$ 1+5=2 \cdot 3 \qquad 1 \cdot 5=2 + 3 .$$ Do you know if there are other integer solutions to $$ a+b=c \cdot d \quad \text{ and } \quad a \cdot b=c+d$$ besides the trivial ...
4
votes
4answers
170 views

Reflected rays /lines bouncing in a circle?

Consider the following situation. You are standing in a room that is perfectly circular with mirrors for walls. You shine a light, a single ray of light, in a random direction. Will the light ever ...
9
votes
0answers
111 views

Interesting shapes using probability and discrete view of a problem

Suppose we have a circle of radius $r$, we show the distance between a point and the center of the circle by $d$. We then choose each point inside the circle with probability $\frac{d}{r}$ , and turn ...
13
votes
3answers
160 views

Can exist an even number greater than $36$ with more even divisors than $36$, all of them being a prime$-1$?

I did a little test today looking for all the numbers such as their even divisors are exactly all of them a prime number minus 1, to verify possible properties of them. These are the first terms, it ...
3
votes
1answer
80 views

What does it mean to suppress a number in math?

What does it mean to suppress a number in math? I was doing a math problem and it said to "suppress a term of a sequence." Does this mean to decrease or get rid of the term? Problem: Let ...
2
votes
0answers
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 ...
12
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10answers
1k views

Small Representations of $2016$

It's the new year at least in my timezone, and to welcome it in, I ask for small representations of the number $2016$. Rules: Choose a single decimal digit ($1,2,\dots,9$), and use this chosen digit, ...
25
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10answers
4k views

Is it possible to draw this picture without lifting the pen?

Some days ago, our math teacher said that he would give a good grade to the first one that will manage to draw this: To draw this without lifting the pen and without tracing the same line more than ...
15
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1answer
317 views

New Year Summation 2016: $\displaystyle\sum_{r=3}^{\; 3^2}r^3$

Decode the following summation to welcome the new year! Find integer $n$ such that $$\large\color{darkblue}{\sum_{\qquad \qquad r={\sum_{m=0}^\infty\left(\frac{n-1}n\right)^m }}^{\qquad \qquad ...
5
votes
2answers
64 views

Issues solving equations involving $x^{x^x…}$?

I stumbled across this problem: $x^{x^{x^{...}}}=2$ Obviously, I used the substitution trick and I got $x^2=2$ and thus, $x=\pm\sqrt{2}$. I have tested that this works. However, I tried to ...
9
votes
1answer
92 views

Relationship between primes and practical numbers

This is my first post here. I am a musician, and not a mathematician, but I enjoy doing things to prime numbers and seeing what comes out. I have defined a sequence which takes the following values ...
0
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1answer
222 views

New year incoming, 2016 [closed]

Here we are, another year is going to finish. Then, what are the "good" or "funny" properties you can find about the number $2016$? Or, is there a natural problem having $2016$ as answer? I tried to ...
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votes
3answers
151 views

Interesting patterns to the algebraic solutions of polynomials [closed]

In yet another attempt to find the solution to the quintic polynomial, I started looking backwards at the solutions to the quartic, cubic, quadratic, and linear polynomials to see if I could pick up ...
13
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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 ...
2
votes
0answers
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 ...
0
votes
1answer
37 views

What is differential time ratio? [closed]

Alright, so I discovered this website detailing some far-out time travel theories. Now, before you say anything let me be clear, I'm not interested in time travel so much as the creative writing ...
2
votes
2answers
65 views

Can this be triangulated?

Given N people with their phones that can sense the signal strength of every other phone knowing what phone it is. Phones don't know their absolute location (underground). There is a formula that ...
47
votes
17answers
2k views

What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?

Good examples would be The Square Root of 2 by David Flannery or Math Girls by Hiroshi Yuki.
0
votes
1answer
72 views

Growth rates slower than logarithmic? [closed]

So far, I've been able to determine growth rates using the following limit:$$\lim_{x\to\infty}\frac{f(x)}{g(x)}$$Which, if need be, can be solved with calculus. From this, I deduced that it is very ...
-2
votes
1answer
34 views

If you invest in an account that earns 4.5% interest compounded continuously.. [closed]

If you invest in an account that earns 4.5% interest compounded continuously, how long will it take to triple your money assumig you leave it in the account? Just another fun question from a website ...
2
votes
2answers
70 views

Otimization on a city with infinite many traffic lights.

Province Ave has infinitely many traffic lights, equally spaced and synchronized. The distance between any two consecutive ones is $1500m$. The traffic light stay green for 1.5 minutes, red for 1 ...
2
votes
5answers
82 views

If $2^{2013}-2^{2012}-2^{2011}+2^{2010} = k \cdot 2^{2010}$, find $k$ [closed]

Hey this is just a question i was having fun with but couldnt solve for some reason. Would love if you can help me solve it thankyou!: If $2^{2013}-2^{2012}-2^{2011}+2^{2010} = k\times2^{2010}$. ...
4
votes
1answer
58 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 ...
39
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2answers
1k views

Xmas Greeting 2015

Simplify the expression below into a seasonal greeting using commonly-used symbols in commonly-used formulas in maths and physics. Colours are purely ornamental! $$\large \begin{align} \frac{ ...
1
vote
3answers
79 views

Integrating $f(x)=\int|\cos(x)|dx$ and then solving $f(x)=\frac {2x}{\pi}$?

I realised the other day that by applying absolute value signs to the cosine function and then integrating, I would get an almost sine function that doesn't have negative slope. And then I also ...
5
votes
1answer
31 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 ...
13
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3answers
138 views

Generating numbers by repeated doubling and digit reversal

Let $S$ be the smallest set of positive integers satisfying the following conditions: $1 \in S$, If $n \in S$ then $2n \in S$, If $n \in S$ then the digit reversal of $n$ is also in $S$. We assume ...
1
vote
2answers
49 views

Does an infinite iteration of a function still have my solution and why does it work?

I found the other day that you could find some solutions to an equation in the form $$f[f(x)]=x$$As a matter of fact, I found some solutions to$$f[f(f(\cdots f(x)\cdots))]=x$$ The solution, if one ...
1
vote
0answers
18 views

Has a simple optimal or provably near optimal strategy been shown for backgammon bearing off?

I aplogize in advance for the somewhat long post. I've tried to split it into manageable paragraphs. So in backgammmon, in the so-called "end-game", both players have their pieces in their respective ...
3
votes
0answers
248 views

Evaluating $\int_{0}^{\infty} \left[\left(\frac{2015}{2015+x}+\cdots +\frac{2}{2+x}+\frac{1}{1+x}-x\right)^{2016}+1 \right] ^{-1}\mathrm{d}x$

I need to evaluate $$\int_{0}^{\infty} \left[\left(\frac{2015}{2015+x}+\cdots +\frac{2}{2+x}+\frac{1}{1+x}-x\right)^{2016}+1 \right] ^{-1}\mathrm{d}x $$ I've been told that the way forward is ...
5
votes
3answers
127 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 ...
4
votes
2answers
89 views

How can one find the zeroes of $f(x)=ae^{bx}+cx+d$?

A certain physics problem I have been working on has turned into a math problem. Particularly, I want to find the solutions of some equation of the form $$f(x)=ae^{bx}+cx+d = 0$$ where $a, b, c,$ ...
2
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2answers
37 views

Multidimensional Riemann integration and notion of volume or Lebesgue theory and notion of measure

I have finished 9 chapters of "Introduction to Analysis" by Maxwell Rosenlicht (1968). The last chapter treats about "Multiple Integrals". I find the notation a bit complicated. Also, author ...
5
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1answer
154 views

Dividing numbers with dots?!

OK. This intrigues me. I recently came across this video. Which presumably tells you how to divide 133,342 with 121 only using hand drawn dots! Fair enough but I don't think this works for every ...
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vote
3answers
35 views

How many definitions of a list of 30 would I need to know so that I could answer at least 10 from any 18?

While studying for my English exam, I noticed that the way the definitions portion of the final is set up posed an interesting problem. While I will study all the definitions, I thought trying to ...
1
vote
1answer
24 views

Number of way that set of point can be colinear

Assume I have $n$ points in a plane. and I want arrange them in the way that for any point at least I can find two other points that are all the three points are collinar. I want to know how many way ...
0
votes
1answer
69 views

How can we draw $14$ squares to obtain an $8 \times 8$ table divided into $64$ unit squares?

How can we draw $14$ squares to obtain an $8\times8$ table divided into $64$ unit squares? Notes: -The squares to be drawn can be of any size. -There will be no drawings outside the table.
4
votes
1answer
97 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
0answers
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 ...