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.

5128 questions
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Does every such sequence enter into a loop?

I was playing around with number sequences and came across the following interesting type of sequences of positive rational numbers: The sequence starts with any rational number $x_1$. Each subsequent term $x_n$ is defined by $x_n=\frac{a+b}{a+1}$…
Moko19
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"implied multiplication" operator precedence?

I hold a masters in computer science from one of the worlds top universities and until today I thought I more or less know basic math. I'm sure you guys all know these click-bait simple "90% of people can't solve this equation" posts on facebook…
matthias_buehlmann
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Are these pointing sequences periodic?

A year or two ago I was fiddling around with sequences and I stumbled upon a family of sequences that seem to have some interesting properties. The family, $\mathcal{S}$, is defined as follows: $$ f\in\mathcal{S} \iff f :…
Sriotchilism O'Zaic
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What times can be measured with two hourglasses?

It is easy to show that if you can only earn $p$ or $q$ coins, with $p$ and $q$ coprimes, the largest number of coins which cannot be earned is $pq-p-q$. If we have two hourglasses that last $p$ and $q$ minutes respectively, the longest number of…
mau
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Milk and Tea problem

There are two cups on a table. One is filled with tea, the other with milk. If we take a spoon of tea from the first cup and place that into the cup with milk and stir and then do the same but vice versa. Which was there more of in the end? Tea in…
McLinux
  • 421
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What is the fewest number of squares required to cover a $11\times13\text{ cm}$ rectangle without overlap?

I need help figuring out this math puzzle: I have a $11\times13\text{ cm}$ rectangle and I need help figuring out the least number of squares I need to cover the rectangle without overlap. I'm told the answer should be at most 5. If you can, provide…
Cheesy cat
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Find all possible values of $ a^3 + b^3$ if $a^2+b^2=ab=4$.

Find all possible values of $a^3 + b^3$ if $a^2+b^2=ab=4$. From $a^3+b^3=(a+b)(a^2-ab+b^2)=(a+b)(4-4)=(a+b)0$. Then we know $a^3+b^3=0$. If $a=b=0$, it is conflict with $a^2+b^2=ab=4$. If $a\neq0$ and $b\neq0$, then $a$ and $b$ should be one…
Incognito Huang
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Folding sheets of paper to measure distances

You have $n\in\mathbb{N}^*$ sheets of paper with dimensions $a,b\in\mathbb{R}_+^*$ that can be folded as many times as needed. What is the set of lengths in $\left]0,\sqrt{a^2+b^2}\right]$ one can measure with those $n$ sheets ? We can assume that a…
Hippalectryon
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Placing numbers around a circle

Is it possible to place the numbers $1,2,\ldots,2014$ around a circle so that any number is divisible by the (positive) difference of its two neighbors? This problem was given to me by my neighbor's daughter, and I couldn't figure it out. I'm…
Jared
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How to win this game?

I have a challenge: to win the game with the following rules: There are exactly two players and their turns alternate; At each turn, a player removes 1, 2, 3 or 4 counters from a pile that was initially 27 counters; The games ends when all…
benedito
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A strange lier that tells truth on 7th day of the week.

Q)Ravi is strange liar. He lies on 6 days of the week, but on the seventh day he always tells the truth. He made the following statements on 3 successive days: Day1: "I lie on Mon and Tue." Day2: "Today, it's Thu, Sat, or Sun" Day3: "I lie on Wed…
Harshal Gajjar
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Can we get a 'good' approximate value of $\sqrt 2$ by an equation which uses each of $1,2,\cdots,9$ once such as $12653\div 8947\approx1.414217$?

I've been interested in representing $\sqrt 2\approx 1.414213562373095$ by an equation which uses each of $1,2,\cdots,9$ once. Suppose that the following conditions must be satisfied. Then, can we get a 'good' approximate value of $\sqrt 2$…
mathlove
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Help explain a new theory on small sines

(10 Mantissa[sin(10^(-100 - r1/x))])^(r2x) The reason for the argument form .10^[-n-(1/x)] is the beautiful pattern found in sin(10^-n) for positive integer n. $$ \begin{array}{| c | r |} \hline n& sin(10^{-n}) \\ \hline \\ \hline 1&…
Marvin Ray Burns
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All Humans have the same gender

This was actually a homework assignment in a math lecture in Germany. We prove with mathematical induction that all humans have the same gender. So consider a room with $n$ people. For $n=1$ the statement is obviously true. Now the inductive step:…
Michael Lehn
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Minimum bits required to identify which square was flipped

The question goes as follows: You are presented with a 8x8 square board, with some of the squares filled with red, and some white. You can study the board for as long as you wish, then look away while another person flips the color of one square.…
Chanhyuk Park
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