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Questions tagged [recreational-mathematics]

Mathematics done just for fun, often disjoint from typical school mathematics curriculum. Also see the [puzzle] and [contest-math] tags.

Recreational mathematics is a general term for mathematical problems studied for the sake of pure intellectual curiosity, or just for the enjoyment of thinking about mathematics, without necessarily having any practical application or expectation of deep theoretical results.

Recreational mathematics problems are often easy to understand even for people without an extensive mathematical education, even if the theory they lead to may turn out to be surprisingly deep. Thus, recreational mathematics can serve to attract the curiosity of non-mathematicians and to inspire them to develop their mathematical skills further.

Many typical recreational mathematics problems fall into the fields of discrete mathematics (combinatorics, elementary number theory, etc.), probability theory and geometry. Important contributors to recreational mathematics are Sam Loyd and Martin Gardner.

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What is the length of the longest possible shortest path on an n × n grid?

Let $M \in \{0, 1\}^{n \times n}$ be a grid. 0 represents a free field, 1 a blocked field. You can move in four directions: up, down, left, right. Given the worst possible start and end position on the worst possible $n \times n$ grid, what is the…
Martin Thoma
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Proving (or not) that two integer valued sequences are equal (featuring $ \lambda(n,k) = n^2 -kn + 1$).

We are going to define two functions $\quad \psi: \{3,4,5,6, \dots \} \to \{4,5,6,7, \dots \}$ and $\quad \rho: \{3,4,5,6, \dots \} \to \{4,5,6,7, \dots \}$ where $\psi$ is defined using an algorithmic specification while $\rho$ is specified using…
CopyPasteIt
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Is braking (e.g. when driving a car) from a non-zero speed to a complete stop in any way related to division by zero?

NOTE: I moved this question here from MathOverflow in accordance to suggestions I received there. It's been many years since my university days, but there is one thing that my mathematics professor once said, which has stuck with me all this…
aoven
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Mental math trick for squared 20s and squared teen numbers?

I'm working on a pullup progression workout. I'd like to mental math how many pull-ups done in one session. I do decrements from $20s$; e.g., $20,19,18,17,16,15,14,13,12,11,10$. This is like the summation version of a factorial, the nth triangular…
adamaero
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What is the solution to this problem in which the goal is to find the best strategy

"There are two prisoners and a jailer who wants to kill them, but in an act of magnanimity the jailer tells them: At your side there is a room with a chessboard wherein each square there is a coin placed randomly (heads or tails), I will enter with…
B.Casals
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Grid translation

I have a 6x6 grid, and in its first cell (row 1, column 1), its value is (-3, 2) and on its last cell (row 6, cell 6), its value is (2, -3). Another values inside this grid are: $(x_0, y_0) => (x_1, y_1)$ (1, 2) => (-2, 2) (1, 3) => (-1, 2) (1, 4)…
VansFannel
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Challenging Mathematical Teasers; Pecking Order

I was going through the book "Challenging Mathematical Teasers" by J.A.H. Hunter, and, of course, I got stumped. Naturally, I went to the solutions part of the book, but here's the kicker, the solution raised more questions. My question is, rather,…
BonInSossusvlei
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A drunk knight's tour

Consider an infinite chess board. A knight moves 2 squares forward on one direction, then turn left or right, move 1 square further on. Let's denote this a normal knight, or $\langle 2,1\rangle$ knight. And it's known that a knight could reach any…
athos
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The Mean of the Range, IQR and SD? Will it give an interesting result?

What if we take the Mean of the three chief measures of spread, i.e Range, Interquartile range, and the Standard deviation? Will it give us an "all-purpose" measure of spread that is very reliable, or will it just be counterproductive and give us…
Ramana
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best cut for microwave oven

Suppose, that there is a Pizza which is round and has radius $1$. Now one would like to find the best way, under $n$ cuts, to cut the Pizza so as to obtain the minimum 'Microwave Oven Distance'- For any point $p$ on the Pizza, its "microwave oven…
athos
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How much faster than a speeding bullet is superman?

I need some help with a problem I want to solve. You have a gunman standing 50 ft away from a human target. According to google, the average bullet travels at 2,500 fps. If my math is correct (debatable, my math skills are kind of sad) this gives…
MarielS
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Finding place of the nine digits

The nine digits 1, 2, 3, ... .., 9 are placed in the nine triangles of the attached figure in such a way that the digits around each circle add up as indicated. Calculate the value of N.
Piquito
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Maximum number of rounds needed for a multiple strike tournament

I have a spreadsheet set up that will allow me to track video game tournaments (although it can be used for other types of tournaments as well). The formulas that I created the spreadsheet with provide an approximate number of rounds needed for the…
Matthew Farnsworth
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Math sticker meanings

I am trying to understand what these stickers mean. The ones on the top row are: Good one! I am impressed! (I know $\sum x_n /n$ is the mean of the $x_i$, but I don't understand this one) The bottom row is: This improvement is a good sign (I…
A. Goodier
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What is the max single day score on jeopardy?

So, I was trying to figure out what the max score on jeopardy is for a single day. what I did was account for the daily doubles at the very end with the lowest value category, (to save on the 1000's), Wagered everything in the daily doubles and…
Rivasa
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