Mathematics Stack Exchange
Mathematics Stack Exchange

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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Rotating position in a square grid

I was asked a question about the following problem (maybe puzzle would be a better word), which originally came from programming. The person, who asked me this, was programming something involving 3-by-3 square. He decided to index the positions on…
Martin Sleziak
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Mandelbrot Set Equation

Is there a graphable equation that graphs the Mandelbrot Set? It seems like an interesting design, but I want to find a way to show all of the details via a graphing calculator.
Jason Chen
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Find the results of the race using the given 5 conditions.

There are five competitor A, B, C, D, and E and they enter a running race that awards gold, silver, and bronze medals. Each of the following compound statements about the race is false, although one of the two clauses in each may be true. 1. A…
Harshal Gajjar
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Formula(/How) to find 2 numbers that add together to give one number and times to give another

I have $2$ numbers $a, b$. I need a formula (or a how to) to find which $2$ numbers $c,d$ will add together to give a and times together to give $b$. So $c + d = a$ $c \cdot d = b$
Jonathan.
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Odd marble out in $m$ weighings on a balance

Thinking that this may be as poorly known as it was $35$ years ago when I first knew the truth - based on How can you pick the odd marble by 3 steps in this case? and others, I pose two closely related questions in one for general edification. You…
Mark Bennet
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How can I find the smallest set such that all even integers $4≤x≤N$ can be written as the sum of two elements in the set?

Given a positive integer N, I want to create a set of positive integers such that any even number $4,6,8,...N$ can be written as the sum of two elements in the set. I also want the set to be as small as possible. For example, with $N=24$, the set…
PhiNotPi
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"Fault tolerant" number guessing

Alice has a hidden random integer $a$ in range $[1, 2^n]$. Each time, Bob can guess a number $x$, and Alice will answer whether $x \ge a$ or $x < a$. However, Alice can give a wrong answer for at most 1 times. In the worst case, how many guesses…
AlumKal
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You dig a hole in Minecraft straight down $n$ blocks, how many blocks must you dig to get out?

I was thinking on this question and came to the solution $3(x-2)$ (where $x$ is the depth of the hole and $x\ge3$) which I am fairly confident in. Although, I wanted to prove it for any hole that is $n$ blocks deep, could anyone illustrate how I…
tothemax
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When is the best date to switch from civilian to military factory production in Hearts of Iron IV?

The video game Hearts of Iron IV is a WWII grand strategy game. One of the most important aspects of this game is industry. There are three types of factories: civilian, military, and dockyards. Ignoring dockyards, civilian factories (commonly…
Matthew Barnes
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Calculator contradicting true statement

There are things called Fermat's near misses. These, according to a regular calculator, are "solutions" to Fermat's Last Theorem. The reason why they're not solutions is simply because there is a limit on how many digits the calculator can…
Alex
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If Sam's age is twice the age Kelly was two years ago, Sam's age in four years will be how many times Kelly's age now?

If Sam's age is twice the age Kelly was two years ago, Sam's age in four years will be how many times Kelly's age now? (A) .5 (B) 1 (C) 1.5 (D) 2 (E) 4 So say at -2 years Sam's age is 12 and Kelly's age is 6. Add one to each year Sam passes. -2 =…
anita
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How do you solve this word problem?

The river is flowing from point A to B at a rate of 15 miles per hour. A boat moves on still water at 45 miles per hour. If it takes David 1 hour and 15 minutes to ride the boat on the river from A to B, how long does it take him to make the return…
anita
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What methods are used to look into $\pi^{\pi^{\pi^\pi}}$ and other stacked towers of repeating irrational numbers?

I recently saw a YouTube video here and it got me thinking, does anyone on this site have any insight on how we would tackle (change to base ten, evaluate, compute, or even put limits on approaching) some things like this? examples: $\displaystyle…
OneCold Ruben
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Suggestions for problem-solving books

I've recently been solving some of the questions in the PROMYS entrance test. I like how the last few problems seem puzzle-like (I mean that you wouldn't expect to find them on a maths exam), but they're still challenging (to me). They don't feel…
rishikesh
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For what natural $n$ does there exist a square composed of $n$ squares?

I recently stumbled upon a cute puzzle involving squares: For what natural $n$ does there exist a square composed of $n$ squares? For example, $1,4,$ and $6$ are valid: But $2$ and $3$ are not valid.
Simply Beautiful Art
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