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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 smallest set $A$ upon which $f(a)$, $a \in A$ must be specified to fully determine $f(x)$, $x \in \mathbb{R}$ if $f(2x)=f(x)$?

Let $f: \mathbb{R} \to \mathbb{R}$ satisfy $f(2x)=f(x)$ and let $A \subset \mathbb{R}$ such that if I then specify $f(a)$, $\forall a \in A$ then $f(x)$ will be defined $\forall x \in \mathbb{R}$. What is the "smallest" set $A$ that satisfies this…
Demonicdrn
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How would you formally describe a common aspect of several recreational river crossing problems?

There are a few river crossing problems that I have seen that share some common aspects. The cannibal and missionary problem is typical. All these problems involve moving everyone from one side of the river to the other side by using a boat to…
user1153980
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Be greater than average joke

The following joke reads "Be greater than average". $$ B > \frac{1}{n} \sum\limits_{i=1}^{n}x_i $$ But as a new and n00b mathematician, I find the syntax difficult to understand and I have a question about it. If the formula for average…
Jimmyt1988
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How do I express 67, 69, 83, 84, 86, 87, 88, 93 with 2,0,2,2 only?

Use $2, 0, 2, 2$ and some mathematical operators to express numbers from $1$ to $100$. Operators: $+$, $-$, $\times $, $\div$, ( ), √ (square root), $^$ (power), $!$ (factorial), $!!$ (double factorial), nr (permutation) , nr (combination) Update:88…
伍逸朗
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When will two cars pass each other

There was a question in my math text book the other day that stated: $2$ cars each travelling at a constant velocity around a ring , complete exactly $4$ and $7$ rounds in one hour. If they start at exactly the same time from the same place but…
simplton
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Formula for adapting a number for cross reference

As a keen cyclist I'm trying to use the Allen Coggan Relative Power table that then relates your Relative Power 'score' to what category rider you are. My question is that given rides/segments/hill climbs are rarely exactly 5 seconds/1 minutes/5…
Mathew Mitchell
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How can I get out from the room alive in this recreational problem(Also known as "brain teasers")?

You are locked in a 50 by 50 by 50-foot room which sits on 100-foot stilts. There is an open window at the corner of the room, near the floor, with a strong hook cemented into the floor by the window. So if you had a 12-foot rope, you could tie one…
Muḥammad Mushfiqur Raḥman
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parameter family of functions $[0,\infty) \to [0,1)$

I'm looking for a parametrized family of functions $f_{a}(x): [0, \infty) \to [0, 1)$ with the following properties monotonically increasing, no inflection points $\forall a$, $f_{a}(0) = 0$ and $\lim_{x\to\infty} f_{a}(x) = 1$ $f_{a}(1/x) = 1 -…
Nico Schlömer
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Approximating square root by sexagesimal fractions

I am reading The Works of Archimedes and I have found the following method for approximating the square root with sexagesimal fractions: Ptolemy has first found the integral part of $\sqrt{4500}$ to be $67$. Now $67^2 = 4489$, so that the remainder…
Michael Munta
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unique real solution to $x + e^x = 0$ has no special properties, right?

Let $a$ be the unique real number such that $a + e^a = 0$. I claim that (1) $a$ is irrational. (Easy enough: If $a$ were rational, then write $a = p/q$ for integers $p,q$. It follows that $e^a = -a$ is rational, and hence $e^p = (e^a)^q$ is also…
atenao
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Dividing a rectangle into pentagons

This has been haunting me for weeks now. It is easy to divide a rectangle to eight (not necessarily identical) convex pentagons. It seems to be impossible to do with less (playing around makes this apparent). However, though I've tried for several…
Shai Deshe
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Existence of solution to $3a^2 = b^2 + c^2 + d^2$ with constraints.

I am searching for solutions to the following equation: $$ 3a^2 = b^2 + c^2 + d^2 \tag{1} $$ where $a,b,c,d$ are distinct positive integers, satisfying $$ ac = bd.\tag{2} $$ I have found solutions to $(1)$ via a search (over odd $a$) under the…
rtb
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Seeking a better skill calculation of a professional Magic: The Gathering player

One of the interesting things about the professional Magic: The Gathering ecosystem is that players who devote their entire lives to being great at the game might have a peak win percentage of 60%-65%. Indeed, the distance between an above average…
Tyler Murry
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What is the angle the car turned?

A car drives a route through town as indicated alongside, crossing square M five times while doing so. How large is the total angle his car turned through when it has completed the route? I just don't understand how the answer is supposed to be…
Ylyk Coitus
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What is sum of occurrences of zeros, at the end of integers, up to number $n$?

What is sum of occurrences of zeros, at the end of integers, up to number $n$ ? Let's call this function $O(n)$ Examples : $1,2,3,4,5,6,7,8,9,10,$so $O(10)=1$ $1,...,20,$ so $O(20)=2$ $O(100)=11$ $O(200)=22$ $O(300)=33$ $O(300)=33$ $O(1000)=111$
Qbik
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