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

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1answer
25 views

Soft Question: Combinatoric reading material

I am curious if anyone can recommend a good introductory text on combinatorics in similar vein as Richard J. Trudeau's Introduction to Graph Theory put out by Dover. For those who have not read it, ...
1
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1answer
40 views

Sharing items to a particular number of people [on hold]

If I have a game where everyone contributes money, but only $n$ ($11$ in this case) people can win. How do I share the winnings such that the prize amounts do not diverge significantly as the amount ...
1
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0answers
43 views

Can 1 be expressed with only irrationals in a non-trivial way?

There is an equation which I found interesting: $1=\phi+\frac{e^{i\pi}}{\phi}$ where $\phi$ is the golden ratio (either its positive or negative value). Are there other ways to express 1 with only ...
3
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0answers
127 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 ...
11
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1answer
178 views

Fibonacci numbers and the nontrivial zeros of the Riemann zeta function

Is this a mathematical coincidence? For $n=1,\dots,7$: $$ \left\lfloor \prod_{k=1}^n \arg\left(\rho_k\right)\right\rfloor = F_{n+1}, $$ where $\arg$ is the complex argument, $\rho_n$ is the $n$th ...
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0answers
16 views

Asymptote (Graphics Language) Dashed Lines? [closed]

In the graphics language Asymptote, is there a way to code dotted lines?
2
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1answer
75 views

Does an Eulerian semi-graceful polyhedral graph exist?

In a graceful graph, the vertices have number values that range from 0 to $n$ and $n$ edges with all values from 1 to $n$ that are differences between the vertex values. Here's a graceful but boring ...
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0answers
25 views

Conjecture on different type of triangle in a complete graph?

How many different triangles are there in $K_5$? The Answer is 35.(The Moscow Mathematics Puzzle) Then I asked what about $K_6$, $K_7$ and so on ...? With my intuition I arrived at this ...
1
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1answer
43 views

Lunchroom Question: primes adding up to counting numbers?

Our lunchtime group got into another math related discussion. I apologize in advance if this isn't a rigorous question, as none of us are professional mathematicians. This is the question: Is it ...
1
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2answers
20 views

Fixed points of iterates of a certain map $\Bbb N \to \Bbb N$

I have stumbled onto chains of numbers that are interesting in that, when they are split up into their digits, summed, squared, and repeating some number of times, yield the original number. This ...
3
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0answers
65 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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0answers
36 views

How comes plotting affine curve as shadows of gray modulo integer resembles its real locus?

Let $f(x,y)$ be polynomial with integer coefficients. Pick integer $n>2$. Let $M$ be $n \times n$ matrix. Set $M_{i,j}=f(i,j) \mod n$. Plot $M$ as bitmap in shadows of gray where larger value is ...
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0answers
12 views

CAT Percentile calculation?

How the percentile score is calculated in CAT? Can anyone exactly score 100 percentile score? How can two or more people score 100 percentile each?
3
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0answers
34 views

Is there a heuristic reason behind this numerical coincidence?

Write $N(m, n; c)$ for the number of $m\times n$ zero-one matrices where each zero is adjacent to precisely $c$ others, where by "adjacent" I mean up/down/left/right but not diagonally. (Notice that ...
0
votes
1answer
40 views

Prove that 5 points lie on the same circle

How do I prove that 5 points lie on the same circle? I know about the theorem that opposite angles in a quadrilateral are supplementary, but how does that help me prove that 5 points lie on the same ...
1
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1answer
44 views

Playing with propositional truth-tables

The following is the truth-table describing the definitions which allow us to establish truth values to composite formulae or molecules, which is nothing new: I had an idea about playing with the ...
8
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1answer
236 views

The case of Captain America's shield: a variation of Alhazen's Billard problem

I'm sure a lot of you are acquainted with Alhazen's Billiard problem, which involves finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in ...
1
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1answer
83 views

Number puzzle : “You can't determine my sum.”

Albert said to Bob, "I have two unequal positive integers; the smaller is at least 2; the larger is at most 25. I will only tell you their product." So he did. Later, Albert has forgotten the numbers ...
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3answers
47 views

Math trinom help [closed]

$9x^2-9$ its like $(3x+3) (3x-3)$ what about $9x^2-35$ ?
8
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1answer
88 views

$\sum_{n=1}^\infty \frac{1}{(n^2-1)!} - \sum_{n=1}^\infty \frac{1}{(7n+1)!}$ is almost $1+1/6$

I've recognized, that $$\mathcal{S} = \sum_{n=1}^\infty \frac{1}{(n^2-1)!} - \sum_{n=1}^\infty \frac{1}{(7n+1)!} \approx 1.1666666666666666666657785992648796$$ which is almost $1+1/6$. I think it is ...
4
votes
1answer
63 views

In what system(s) of numeration is 11111 a perfect square?

From Charles Trigg's "Mathematical Quickies: 270 Stimulating Problems with Solutions": In what system(s) of numeration is 11111 a perfect square? I have found one base that works: 3. I am not ...
3
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2answers
60 views

Proving the rules of a complicated game are well defined

What strategy could one use to formally model a game and prove that the rules do not lead to any self contradiction? A major example that comes to mind is Magic the Gathering. The card ...
0
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1answer
25 views

3d parametric spiral to 3D goldean mean spiral

I know I can create a 3d parametric spiral with the formula below but How can I do the same thing with goldean spiral? I looked at https://en.wikipedia.org/wiki/Golden_spiral but I don't see how to ...
4
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0answers
52 views

Are all powers of 5 Friedman numbers?

Powers of 5 seem to have a quite interesting property. Not only do the all seem to be Friedman numbers in base 10, it also seems that they don't require digit concatenation and they their 'Friedman ...
4
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0answers
79 views

Puzzles and topology

I like problem solving. In fact, that is the reason I wanted to study mathematics; This is a field where I could learn the underlying logic of the results rather than just learning ideas even the ...
1
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1answer
50 views

Expression as an integral

In order to calculate the pension you can use this expression: $\text{amount}(1+\dfrac{\text{rate}}{100})^y$ where $y$ is years. Set $x=1+\dfrac{\text{rate}}{100}$ you count the amount of money ...
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0answers
6 views

Convert time to decimal (remainders in blocks of 30min)

I've been debating this with my dad for a while and I honestly don't see any possible way to do this using any mathematical method that I know, but I thought perhaps someone else might know more on ...
0
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1answer
21 views

Predictability of what $\lfloor n\log n\rfloor$ “skips”

TL;DR: is there any way to tell what numbers will not be present in the function $\lfloor n\log n\rfloor$ under a given upperbound? I am writing a program that will calculate the sum of the gaps in ...
1
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2answers
65 views

Ghosts closing and opening doors [duplicate]

There are $1000$ doors $D_1,D_2,D_3,\dots,D_{1000}$ and $1000$ persons $P_1,P_2,\dots,P_{1000}$. Initially all the doors were closed. Person $P_1$ goes and opens all the doors. Then person $P_2$ ...
2
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0answers
78 views

Is there a formula for $1+\sqrt{2}+\sqrt{3}+\cdots+\sqrt{N}$? [duplicate]

Is there a known formula to the sum $$1+\sqrt{2}+\sqrt{3}+\cdots+\sqrt{N}$$ where $N$ is some natural number? Thanks
0
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2answers
43 views

Which numbers are square modulo 9? [closed]

How can I prove that n = $1,4,7,9$ for every integer k such that $k^2 = n$ (mod9)?
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2answers
509 views

Proof of a discovery involving the square of whole numbers

It was probably discovered by someone else but: When you take the square of a non-zero whole number the sum of the numbers digit is always equal to $1,4,7,9$ How can I write a mathematical proof of ...
2
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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
2answers
61 views

Triangle Area problem

I've been trying to solve the following: Let $ABC$ be a triangle with sides $a, b $ and $ c$, inradius $r$ and exradii $r_a, r_b$ and $r_c$. If $A'B'C'$ is another triangle with sides $\sqrt{a}, ...
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1answer
44 views

The answer is as expected, but this is not proportionality.

A man leaves office everyday at 5 p.m. His driver leaves home everyday at such a time that he can pick up his master from the office at 5 p.m. The driver drives at a constant speed. Now one day, the ...
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0answers
26 views

Logical Questionnaire [duplicate]

I have to go to shop but I don't have money so I borrowed \$$1000$ from friend A and \$$500$ from another friend B but on my way to shop I lost \$$1000$ and I only have \$$500$ remaining. Out of ...
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3answers
144 views

A set of cards from which I can identify and number $n$ with $1\le n\le N$

I am working with a collection of cards. On each card is written a set of numbers $1\le n\le N$ in ascending order. When I arrange the cards in lexicographic order on the table, no two adjacent cards ...
5
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0answers
103 views

Approximating $\pi$ by an expression of the form $\sqrt{\sqrt{ \cdots \sqrt{ n!! \cdots !}}}$

Here is a problem that appeared as a prize challenge in a periodical for science students, back when I was a student: Find an approximation of $\pi$ formed of the numbers $0$ through $9$, each used ...
2
votes
1answer
126 views

The largest tile in 2048, groups of 3 variant?

Question closed on SO for being too mathematical, I've re-asked it here. Following the rules of the, as http://arxiv.org/pdf/1501.03837v1.pdf puts it, "slide and merge" game 2048, canonically ...
4
votes
3answers
72 views

Does other solutions exist for $29x+30y+31z = 366$?

I was asked this trick question: If $29x + 30y + 31z = 366$ then what is $x+y+z=?$ The answer is $12$ and it is said to be so because $29$ , $30$ and $31$ are respectively the number of days of ...
8
votes
1answer
50 views

Number of lines to connect $n \times n$ dots

The following is a popular riddle: Draw a $3 \times 3$ grid, and connect all the dots using only $4$ straight consecutive lines. The solution is to think outside of the box and do the ...
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0answers
25 views

Active partner in a partnership (active for a few months only)

X, Y and Z start a venture together. Y and Z invest \$4000 and \$3000 respectively while X invests \$1000 initially and after 6 months withdraws his capital and decides to work as a working partner ...
0
votes
1answer
51 views

What is this problem called - 4 blocks and 3 rods?

I can't seem to recall the name of this problem however, I do remember part of its description. Basically, there are three 3 rods similar to those of an abacus and on one of the rods there are 4 ...
8
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1answer
240 views

Digit Code Combination Problem

Based on real life experience, I just considered the following combinatorial challenge: In a workplace with currently $n$ employees each employee has its own unique 4-digit code used to pass ...
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1answer
36 views

Is possible to embed “Print gallery” of Escher in a Klein bottle? [closed]

Looking for ways to filling the void or the central vertex, I found http://www.ams.org/notices/200304/fea-escher.pdf , as one alternative. Now I'm wondering if is possible to embed that Escher's ...
0
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1answer
30 views

How can I find the value of y given x using matlab / octave

I have two points on a plot point1=(40,5) and point2=(50,1) How can I find the value of y given x=42.5 I know y is 4 by looking at the plot but is there away to calculate the y value directly. I ...
3
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1answer
64 views

The Regular Pentagram

Consider a regular pentagon circumscribed in a circle. Connect each vertex of this pentagon to every other not adjacent to it with a straight line segment to obtain a pentagram which contains a ...
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2answers
40 views

Spheres inside a cone - Geometric mean

If you have an odd number of balls (all touching each other) inside a cone so that they all touch the curved wall of the cone, why is the radius of the central ball the geometric mean of the radii of ...
0
votes
1answer
36 views

how many hexagons can be found in the graph?

At first sight I thought that this question requires considering different cases, but I find it difficult to convince myself as to how to start this question. Could someone please give me some ...
1
vote
3answers
45 views

Finding when list of numbers reach periodicity given known values

I'm trying to figure out when numbers reach "periodicity" given known values. I've included an example below with image: I have known sizes (100, 75, and 50) that I would like to know how many times ...