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

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6
votes
2answers
973 views

Sailors, monkey and coconuts

Five sailors and a monkey were shipwrecked on a deserted island, and they spent the first day gathering coconuts for food, piled them all up together and went to bed. But when they were all asleep one ...
1
vote
3answers
124 views

Help on French Math Education Paper

I am looking for very basic (probably I should say very elementary) papers in french designed for elementary school teachers and elementary school educators. I would appreciate if someone can provide ...
2
votes
0answers
123 views

A system of linear equations in integer squares - solvable?

I consider this more a "recreational math" problem, possibly lacking a solution (because it stems from the question of "magic square of squares") or simply intractable with reasonable effort. ...
11
votes
3answers
547 views

Arc sums for a circle of $k$ positive integers whose total sum is $n$

This problem got me thinking about the following more general scenario: Suppose you have $k$ positive integers with total sum $n$, and you arrange them in a circle. Given such an arrangement, you ...
6
votes
2answers
274 views

Concise naming-scheme for polyominoes

There is a neat naming scheme for pentominoes based on letters they resemble. Is there a generalized naming scheme for polyominoes? If there isn't a canonical one, can you think of a good one? ...
6
votes
1answer
4k views

Expected number of calls for bingo win

Before I begin, I did a search through math.stackexchange and came across two previous attempts to get people to solve probability problems involving bingo. Neither produced a response. So what ...
-1
votes
1answer
195 views

Buddhabrot Sewing machine [closed]

The Buddhabrot fractal traces the orbits of the points outside the Mandelbrot set. What design considerations need to be taken into account to create a computerised sewing machine that traces out ...
9
votes
1answer
250 views

Is the number of alternating primes infinite?

I'm not sure if the recreational-mathematics tag is appropriate, but this problem came up during a practice Putnam seminar so maybe? The problem: Say that a positive integer is alternating if ...
5
votes
3answers
1k views

Cyclic sums — How do you use them?

Can someone give me an example of how cyclic sums are used? I don't really understand how they're used in problem-solving. For example, $$\sum_{a,b,c}a^2$$ Any help would be appreciated, and I'm not ...
11
votes
2answers
900 views

Is there a collection of alternative mathematical notation? (Semi-soft Question)

I'm interested in alternative systems of notation for mathematics. I've often heard how mathematical notation is illogical, inconsistent, filled with grandfather clauses that serve no purpose, and ...
2
votes
1answer
76 views

Question on pathological sine function

Some years ago I came across what was defined as "pathological" function defined as: $$ f(x)=\sum_{k=1}^\infty \frac{1}{k^2}\cdot \sin\left(k!\cdot x\right) $$ It was mentioned (in an article I ...
15
votes
5answers
1k views

Is high school contest math useful after high school?

I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
5
votes
4answers
154 views

Example of a question that would seem not to have enough information for an answer

Looking for an example of a question that would seem not to have sufficient information for an answer, or a question that the solution would not require (or maybe even maybe hindered ) by the extra ...
9
votes
0answers
169 views

Number of circles in configuration

Consider the $n^2$ lattice points $(i, j)$, where $1 \leq i, j \leq n$. Let the number of circles that pass through at least 3 points of this set be $C(n)$. What is a good way to count this? Is there ...
1
vote
2answers
420 views

How many ways to write one million as a product of three integers?

In how many ways can the number 1;000;000 (one million) be written as the product of three positive integers $a, b, c,$ where $a \le b \le c$? (A) 139 (B) 196 (C) 219 (D) 784 (E) None of the ...
1
vote
1answer
109 views

Discrete Maths question

Show that $S=\{1,3,4,5,9\}$ is a difference set for $\Bbb Z_{11}$. Identify the design produced from $S$ by the sets of the form $S+i$, $i \in\Bbb Z_{11}$.
12
votes
1answer
206 views

Request for a proof of the following continued-fraction identity

I have been poring over many texts about continued fractions, but none of them seem to be helping me to prove the following beautiful continued-fraction identity (I am nowhere close): $$ ...
2
votes
2answers
3k views

How can you construct as many intersections as possible with n lines?

If you have $n$ lines, it seems to be obvious that you can have at most $\frac{n^2-n}{2}$ intersections: $n = 1$: Obviously you need two lines to intersect, so the maximum number of intersections is ...
1
vote
1answer
506 views

Puzzle of $N$ men around a table

This was asked to me by a friend. $N$ men sit around a circular table. Man 1 has a sword with him and he kills the Man 2, Man 3 picks up this sword and kills the next person i.e. Man 4. Thus the man ...
0
votes
1answer
216 views

How to solve this algorithmic puzzle?

For fixed integers $T\geq G>1$, we say a list $[a_1, a_2,\cdots, a_n]$ is normal if every consecutive sublist $[a_i, a_{i+1}, \cdots a_{i+T-1}]$ of length $T$ has less than $G$ maximal elements. ...
4
votes
1answer
154 views

Prove that all combinators must fulfill A x = x for some x, given that M x = x x and composability of any two combinators

I'm working through Raymond Smullyan's "To Mock a Mockingbird" and I'm stuck on the first problem in the combinatory logic section. I'd appreciate hints, but no spoilers please. The problem is ...
12
votes
1answer
272 views

The number of prime years in a lifetime

$2013$ is not a prime: $3 \times 11 \times 61$. I was born in a prime year, and if I live as expected according to the statistics for U.S. males, I will just reach another prime year, $2027$. That ...
7
votes
3answers
161 views

Trouble simplifying a tough equation

I'm having trouble simplifying the following equation. I've tried grouping terms in different ways, but it's not looking any more joyful. Can someone please help with its resolution? Hopefully by ...
5
votes
1answer
328 views

How is tessellation defined in Mathematics?

Hi. I am a GCSE student and I am interested in Maths. I read few books on maths and learned some mathematical analysis. I know of convergent series but I would like to know how identical sets(not ...
2
votes
3answers
133 views

Pat the Mathemamagician Part 2

Sal the Magician asks you to pick any five cards from a standard deck. You do so, and then hand them to Sal’s assistant Pat. Then you pick one of the five cards, and Pat puts it back into the deck, ...
3
votes
0answers
136 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 ...
6
votes
3answers
304 views

Palindrome of numbers from 1-n

A palindrome is a number or word that is the same when read forward and backward, for example, “176671” and “civic.” Can the number obtained by writing the numbers from 1 to n in order (n > 1) be a ...
1
vote
1answer
48 views

How to get range of 1 to 10 by index?

I have a collection of lessons divided by levels Each level has 10 chapters. ...
83
votes
3answers
8k views

Topology: The Board Game

Edit: I've drawn up some different rules, a map and some cards for playing an actual version of the game. They're available at my personal website with a Creative Commons Attribution 4.0 license. ...
1
vote
3answers
583 views

$5n+1$, $3n-1$ problem, smallest repeating cycle and Collatz conjecture

Among the Collatz conjecture we have other "similar" problems that are solved and have repeating cycles. $5n+1$ has the repeating cycle $13, 66, 33, 166, 83, 416, 208, 104, 52, 26$, with a length of ...
5
votes
3answers
228 views

What is the value of D here?

Number $S$ is obtained by squaring the sum of digits of a two digit number $D$. If the difference between $S$ and $D$ is $27$, then the two digit number $D$ is? My thoughts: Let the two digit number ...
1
vote
2answers
249 views

$N \equiv 3 (\textrm{mod } 4)$ and Collatz conjecture

Can the Collatz conjecture also be interpreted as behaviour, transformation of number of form $N\equiv 3(\textrm{mod }4)$ to the form of $N\equiv 1(\textrm{mod }4)$ Because integers of the form ...
2
votes
1answer
246 views

Dissection of a chess board into 4 congruent pieces

Consider a standard $8\times 8$ chessboard where a pawn is placed on each of the squares $d1,d2,d3,d4$ . Dissect the board into $4$ congruent pieces (reflections are allowed) such that each piece ...
3
votes
2answers
61 views

Calculating the most efficient number of group payment transactions required

If you have a group of people who purchase items together and split the costs (not always evenly). How can you calculate the most efficient number of transactions required to settle outstanding debt. ...
0
votes
4answers
389 views

A logic puzzle from TES: Arena

Its nice when games have riddles hidden in them. While playing TES:Arena, I came across an unusual logical puzzle: There are 3 cells. If Cell 3 holds worthless brass, Cell 2 holds the gold key. If ...
18
votes
1answer
395 views

Mathematical Quine

I have recently discovered that I can create letters and any shape I want by hiding parts of curves by making them complex. To generalise if I want $x>a$ then I multiply my function by ...
6
votes
2answers
1k views

Useless math that become useful

I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless. My idea is to amend my article with some theories that seemed useless when they are created but ...
2
votes
1answer
1k views

In how many ways ( using only whole numbers ) can we divide 49 into 6 parts so that we can obtain any number between 1 to 49?

The series which forms the basis of all the other series is:- 1,2,4,8,16,18. Some other combinations are:- 1,2,3,7,14,22 ; 1,2,4,7,15,20 ; 1,2,4,8,13,21. However, I obtained the basic combination by ...
8
votes
2answers
549 views

What is the most unfair set of three nontransitive dice?

In a set nontransitive dice, each die is superior to another die, but is inferior to a third. It is similar to the game of rock-paper-scissors. Here is one example: ...
5
votes
3answers
300 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, 华罗庚) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
20
votes
1answer
1k views

The $n$ Immortals problem.

I saw this riddle posted on reddit a long time ago, called the "Seven Immortals." In the beginning, the world is inhabited by seven immortals, ageless and sexless, who begin to multiply and ...
14
votes
1answer
739 views

“$n$-Yahtzee” question

Suppose that you have $n \geq 1$ standard 6-sided dice. If all the dice display the same number, we call this an $n$-Yahtzee. Follow this algorithm: Roll all the dice. Set aside those dice with ...
3
votes
1answer
134 views

Monty Hall Application

Driver A comes to a 3 way path junction but is not sure which one to take. Just as he decides to take path 1, a cyclist came by and told driver A all he knows is that he is going on path 3 which would ...
3
votes
2answers
356 views

What are good methods for solving Conway's card-stacking puzzle?

Suppose there is a table with three marked spots, $A, B, $ and $C$, on which playing cards can be put, face up. Initially, an ace (1), a deuce (2), and a trey (3) are placed on one or more of these ...
5
votes
1answer
234 views

asymptotics of the square indicator sum for subsequences of digits

Introduce the function $g(n)$ defined for positive integer arguments $n$ as the count of squares of positive integers among the numbers that can be formed by taking some subsequence of the digits of ...
0
votes
1answer
102 views

finding average price of two lots of shares

Sorry, not a math guy, this might be an overly simple question for the lot of you, but it's a calculation that I'll have to do a lot possibly, so please show me the best way to do it. If I have $1265$ ...
0
votes
4answers
135 views

Is there a theorem that disproves this or is this just some made up meaningless thing?

I find this slightly funny. I saw this on a meme:$$\begin{align}a=x\\ a+a=a+x\\ 2a=a+x\\ 2a-2x=a+x-2x\\ 2(a-x)=a+x-2x\\ 2(a-x)=a-x\\ 2=1\end{align}$$ How can these strange algebraic manipulations not ...
2
votes
1answer
427 views

finding nearest perfect square for a fractional number

Is it possible to have a clear definition for the nearest perfect square number for a fractional number? For example, let us consider a number 0.004. What is another decimal number closest to it, that ...
3
votes
3answers
103 views

What is the smallest number which begins with 7 and if you bring the 7 to the least significant position it becomes a third of the original number?

First I wrote the equation: $7\times 10^2+c_1\times10^1+c_0\times10^0 = 3(100c_1+10c_0+7)$ which becomes $679=290c_1+29c_0$ Then I try fix as many variables as possible. In this first iteration, ...
1
vote
2answers
260 views

Is my proof that the medians of a triangle are concurrent valid?

Consider any triangle ABC. Connect the midpoints of each of the three sides. The inscribed triangle is equal to the other three triangles and they are all congruent. It turns out that the medians of ...