# Tagged Questions

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

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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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? ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $S+i$, $i \in\Bbb Z_{11}$.
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### 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 ...
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, ...