Tagged Questions

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

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0
votes
1answer
29 views

Mathematical reasons for hull design relative to sustainable angle of heel

I've recently been doing a comparative study of ancient Sumerian mythology relative to the book of Genesis. I am curious if there is a way to explain mathematically why a circular, square (cubic) or ...
1
vote
0answers
49 views

Game idea “square or not”

I have an idea of a quadrilateral / square game, and am looking for help. For the moment lets call it the "Square or Not " game. Imagine we have a big stack of cards with on each card some property ...
0
votes
1answer
39 views

Concatenating squares - is this solution unique?

This question asks about concatenated squares to make a square number. For example $[4][9]=49, [16][9]=169, [3136][441]=3136441, [64][009]=64009$ I've been doing a bit of investigating for the case ...
1
vote
0answers
37 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 ...
0
votes
2answers
29 views

replacing numbers to get final anser

I found this question in a random problem solving book that I was reading and wanted to know how you would solve it. I am not sure as how to go about this. Take any positive integer $n$ with fewer ...
1
vote
0answers
42 views

Which numbers have the sum of their digits equal to the sum of the digits of their inverse?

$n$ is a number such as $n \in \mathbb{N}$ and $n >0$.(Eg. $n = 8$) $p$ is the sum of the digits of $n$ in base $10$.(Eg. $n=80$, $a = 8+0 = 8$) $q$ is the sum of the digits of $1/n$ in base ...
2
votes
1answer
64 views

How to conceptualize unintuitive topology?

I found Project Origami: Activities for Exploring Mathematics in my university's library the other day and quickly FUBAR'd (folded-up beyond all recognition) the couple sheets of paper I had with me ...
1
vote
0answers
16 views

Has the mathematics of 4d-tetris, or any other 4-dimensional polyforms been studied?

There are a few variations of 4d tetris games floating around the internet, but I'm more interested to know if there's been mathematical research done in the area of 4d polyforms. I assume that the ...
2
votes
1answer
34 views

Pig Wheel question

A friend of mine was playing the bar game Pig Wheel recently and posed some interesting questions to me. He was playing with others as a group of four and, acting collectively, they came out about ...
3
votes
1answer
61 views

Finding out a person's age in days given their birthday dd/mm/yyyy?

It has to be somebody alive today. Assume that the day is today - September 15, 2014. This is convenient because the leap years will be regular (once every for years; the weird rule applies to $1900$ ...
3
votes
0answers
51 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 ...
3
votes
1answer
103 views

Is there a prime number ending with the natural number $n$

if $n$ not is divisible by 2 or 5? Example: given 813075843967837637675737563754361301, there is a prime 20813075843967837637675737563754361301 or given ...
0
votes
1answer
33 views

Integer solutions of an equation that is set to a number

How many integer solutions for $a$ and $b$ in $(ab)/(a+b)=3600$? My attempt: $(ab)/(a+b)=3600$ = $ab=3600(a+b)$ = $ab=3600a+3600b$ =$ab=3600a=3600b$ Dividing $3600b$ on both sides ...
3
votes
3answers
120 views

Summing infinitely many numbers: how to assign a value?

If we take $S = 1-1+1-1+1-1+1-1+...$ we can show (in many different ways) that the result of the sum is $\frac{1}{2}$. One way for example would be to add $S$ to itself but shift it along one place, ...
2
votes
1answer
71 views

How are Sudoku puzzles created?

I recently read about the connection between solving Sudoku puzzles (and other graph coloring problems) and Groebner bases. This doesn't lead to an efficient solution technique, but it does link a ...
0
votes
0answers
143 views

Prime number distribution theory for dummies

For the distribution of prime numbers there is a hypothesis which predicts the possible positions of prime numbers called Riemann hypothesis ...
2
votes
3answers
107 views

Fun proofs for layperson?

I'm not quite sure whether this question belongs here, because it has no definite answer. But I'll give it a shot. If any of the mods objects, then I will, of course, respectfully delete this ...
2
votes
1answer
78 views

Mathematics of paper fold-cutting

Take a square of paper... ... and fold it any number of times using consecutive straight folds... ... then cut off any number of pieces using consecutive straight cuts... ... and unfold the ...
0
votes
0answers
30 views

Limiting behaviour of a system

A friend of mine offered me the following problem. Suppose we have a rabbit and a fox in $\Bbb R^2$. The rabbit starts at time $t=0$ at the point $(0,0)$ and runs with constant speed $(1,0)$. The fox ...
5
votes
2answers
217 views

What is the flaw in this proof that all triangles are isosceles?

What is the flaw in this "proof" that all triangles are isosceles? From the linked page: One well-known illustration of the logical fallacies to which Euclid's methods are vulnerable (or at least ...
-2
votes
1answer
31 views

Equation that outputs digit in 1's 10's 100's slot [duplicate]

I need an equation that outputs the digit in the slot of my choosing EX1: I want the 10's slot in 1837 EX2: I want the 10's slot in 123456789 EX3: I want the 1000's slot in 93037352 I also need it ...
-2
votes
1answer
36 views

Challenge - “Highscore” output equation

I need an equation capable of processing 2 inputs to make one output that is either = to input 1 or 2. This is how it works. Since it is working with scores and such, Input1 will be "Last Score", and ...
21
votes
10answers
3k views

Get $5$ by doing any operations with four $7$s

How can one combine four sevens with elementary operations to get $5$? For example $$\dfrac{(7+7)\times7}{7}$$ (though that does not equal $5$). I am not able to do this. Can you solve it or prove ...
-5
votes
1answer
100 views

Is it possible to make a 3dimensional parametric plot of this curve that looks lika a UFO?

The solution set of $$ y (x^2y+y^3-x^2-4y) = 1 $$ Looks like ** How would the parametric plot in 3d look like (in an appropriate intervall)?
0
votes
1answer
37 views

Form $4$ new symbols with the most common symbols

Suppose we have $6$ symbols, say $A,B,C,D,E,F$. We are asked to form $4$ new symbols using the $6$ symbols with the addition operation. For example, the $4$ new symbols can be $A+C+E, F+E+A, ...
1
vote
0answers
73 views

Folding sheets of paper

You have $n\in\mathbb{N}^*$ sheets of paper with dimensions $a,b\in\mathbb{R}_+^*$ that can be folded as many times as needed. What is the set of lengths in $\left]0,\sqrt{a^2+b^2}\right]$ one ...
0
votes
2answers
112 views

Reciprocal of 81 being the sequence of all natural numbers?

According to this document: http://www.answering-christianity.com/fakir60/81.htm describing the theory of scientist Peter Plichta, the reciprocal of 81 is: the ...
6
votes
0answers
107 views

Mathematics of the Ice Bucket Challenge

I've been considering the mathematics of the now global ice bucket challenge. Simple model In the simplest incarnation, there is one original seed, who then nominates 3 others, each of which take ...
0
votes
3answers
48 views

Completing the square for a quartic expression

By completing the square, find (for real $x$) the minimum value of: $$x^4 + 2x^2 + 2.$$
1
vote
2answers
120 views

Proving that an equilateral triangle in the plane cannot have vertices on integer lattice points

Thanks for the help! I've written a more detailed proof. The hints were great.
1
vote
2answers
48 views

Proper way to express 0 in this case?

If 0=(x-a)(x-b)(x-c)...(x-x)..=0. So it's a product sum that we write with pi instead of sigma but how? There should be indexes but I'm not convinced that I understand what notation to use. $$\prod_{ ...
3
votes
1answer
51 views

Tiling squares with L-Trominoes

Is there a simple proof that any square besides a 3x3 square with area divisible by 3 is tileable with L-trominos?
-1
votes
2answers
90 views

3D Geometry Problem

If we have 4 equal sized spheres with radius $R$ arranged surrounding another smaller sphere such as to make a triangular pyramid from the centers of the $4$ spheres with radius $R$. The radius of ...
1
vote
1answer
51 views

What is the numeral system which uses the number of digits as a signifier of value called?

Our standard notation of representing numbers has an implied infinite number of zero digits on the left of all numbers. 42, 042 and 00000000042 all represent the same number. I'm thinking of the ...
1
vote
0answers
34 views

Are (odd) perfect numbers divisible by a repdigit (in another base)? How about by a repunit?

[This has been cross-posted to MO.] A positive integer $N$ is said to be a perfect number if $$\sigma(N) = 2N,$$ where $\sigma(x)$ is the sum of the divisors of $x$. For example, $6$ is perfect ...
15
votes
16answers
1k views

Beautiful, simple proofs worthy of writing on this beautiful glass door [closed]

What are some of the more beautiful proofs you know? I am measuring beauty in two dimensions -- first, how conceptually elegant is it and second, how aesthetically pleasing is it. Context: I work ...
6
votes
2answers
84 views

Winning strategies in multidimensional tic-tac-toe

This question is a result of having too much free time years ago during military service. One of the many pastimes was playing tic-tac-toe in varying grid sizes and dimensions, and it lead me to a ...
0
votes
1answer
80 views

I'm not understanding this puzzle [closed]

At first, I was thinking, mininmum amount of sticks it takes to create the figure, and then how many draw strokes it takes to create the boxes without crossing paths...but I can't figure out what's ...
1
vote
0answers
53 views

Primes made from sequential digits

While messing around, I noticed that across some prime numbers contain only sequentially increasing digits, e.g. $23, 67, 89,23456789$. If we adopt a convention of returning to $1$ after a $9$, we ...
9
votes
2answers
178 views

Good Reference for Justifying (less well-known fields of) Math?

How do we as mathematicians justify the study of math to students? Or, indeed, how do we justify it to the general public? How do you justify your particular field? I'm particularly interested in ...
1
vote
2answers
59 views

4 crystal balls and a 10,000 story building

There is an analog of this question I've heard with 2 crystal balls but a higher number like 4 or more makes it much more interesting. You are given 4 crystal balls and there is a 10,000 story ...
0
votes
3answers
174 views

Blue Eyes: A Logic Puzzle, has a puzzling solution (a.k.a. What does common knowledge have to do with it?)

In Blue eyes: a logic puzzle (specifically, the follow up questions), the most common answer is that it needs to be common knowledge that someone has blue eyes for all the blue-eyed people to leave. ...
26
votes
7answers
2k views

Mathematical literature to lose yourself in

H.M. Edwards in the preface to his book on the Riemann Zeta Function, summarises his philosophy on learning Mathematics: ...I have tried to say to students of mathematics that they should read the ...
4
votes
2answers
83 views

Natural numbers verifying $P(n) = n^2 - 42n + 440$, where $P(n)$ is the product of the digits

Let $P(n)$ be the product of the digits of the number $n$, with $n \in \mathbb{N}$. What is the product of all the natural numbers $n$ that verify the equation $P(n) = n^2 - 42n + 440$? I ...
12
votes
1answer
272 views

Joke explanation: “a comathematician is a device for turning cotheorems into ffee”

Ok, so apparently there is an old joke (which I DO get) that says that in Hungary a mathematician is a device for turning coffee into theorems. I found a post by Qiaochu Yuan that has the following ...
2
votes
1answer
35 views

Csn someone produce a sudoku puzzle where guessing more than one cell's value at a time is required?

Currently I have a sudoku puzzle solver program and I've tried all the puzzles I can find that are labeled the "hardest" on various sudoku video games and puzzle books. My solver has solved them all. ...
4
votes
0answers
83 views

Binomial triplets

Solutions to the equation $$\dbinom{a}{n}+\dbinom{b}{n}=\dbinom{c}{n}$$ I will refer to as 'Binomial triplets of order $n$'. These triplets describe simplicial $n$-polytopic numbers that can be ...
9
votes
1answer
106 views

Can 23 of this polycube fit in a 5x5x5 box?

Consider the following pentacube (front and back view shown.) I have used Burr Tools to determine that 24 of these will NOT fit in a 5x5x5 box. According to my notes when working on this problem a ...
23
votes
1answer
237 views

Which is greater, $20 \uparrow\uparrow\uparrow\uparrow 20$ or $4 \uparrow\uparrow\uparrow\uparrow\uparrow 4$?

This past Wednesday's What-If had this image at the bottom: In particular, I am interested in $20 \uparrow\uparrow\uparrow\uparrow 20$. I immediately thought of Graham's Number, but clearly that ...
1
vote
1answer
51 views

Why does the filling up of odd order magic square with numbers follow the knight movement?

Why does the filling up of odd order magic square with numbers follow the knight movement? I was reading about magic square, where I came up with the knight movement filling up of the magic square ...