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 minimum number of squares to be drawn on a paper in order to obtain an 8x8 table divided into 64 unit squares?

What is the minimum number of squares to be drawn on a paper in order to obtain an $8\times8$ table divided into $64$ unit squares. Notes: -The squares to be drawn can be of any size. -There will be no drawings outside the table.…
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Hamiltonian path on a chessboard with prescribed endpoints

On an 8 x 8 chessboard consider two squares to be adjacent if and only if they share a common side. All paths below will consist of steps which join one square to an adjacent one. Under these conditions it is easy to construct a Hamiltonian cycle…
user2052
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A formula with only one $0$ that evaluates to a given integer

Just found this math puzzle online: Original puzzle: Using one zero (and no other numbers) and mathematical (including trigonometric and advanced) operations, how can you achieve a final result of 6? Advanced one: Using only trigonometric…
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Two formulae for $\pi$, probably known?

I stumbled upon (in the literature) two identities for $\pi$, but they were not referenced as they are probably well-known. Hoping someone could point out who found them first. Basically, the relations are: $$\sum_{p=0}^{\lceil M/2\rceil-1}\frac{2…
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Setting up an English pool table

A friend and I were playing some English pool yesterday. When you rack the balls it has the specific set up in the picture where the 8 ball must be in that central position and the balls are laid out either as in the picture OR the opposite way…
Mike Miller
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A recreational math problem, integers in a grid

I was thinking of the following recreational math problem: We have a $4\times 4$ square filled with integers $a_{1,1},...,a_{4,4}$. It has $30$ sub-squares $A_{i,j,k}$, corners of the form $a_{i,j},a_{i,j+k},a_{i+k,j}, a_{i+k,j+k}$, such that sum of…
student
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Starting for Self Study of Mathematics

I am a Mathematics enthusiast but after High School i took a job. Now i want to do self study in mathematics and to dive deep into the subject. What should i do ? What books and articles should i read?
Renil Babu
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Covering eleven dots in the plane with eleven coins - counterexample?

The questions here and here relate to the question as to whether, given ten equally sized coins and a configuration of ten dots in the plane, there is a way of placing the coins so that they cover all the dots without overlapping. The solution given…
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Is it known whether a constant $A$ exists, such that there is always a Carmichael-number between $x$ and $Ax$ for $x\ge 561$?

For prime numbers, such a constant is well known. For $n\ge 2$, there is always a prime between $n$ and $2n$, so $A=2$ does the job. Carmichael-numbers are much rarer, so I wonder, whether a constant $A$ has been found and be proven to do the job…
Peter
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What is the Mathematics behind the folding an A4 sheet in 3 equal parts??

This is an extension question of this question. They have given a plenty nice way to fold a A4 sheet in 3 equal parts. What is the Mathematics behind the foldings? Can we use the same way for $A5,A6,\ldots$?
David
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Alien Mathematics

I'd like to pose the community here a challenge. It's often supposed that if we encounter intelligent alien life, mathematics will probably be how we start communicating. We have seen Rosetta-stone-type codebreaking, which depends on assuming some…
spraff
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Simple question about dividing by zero, $y=\frac{x}{x}$ when $x=0$

Is there a rule that says you have to simplify equations before evaluating them? Would $y=\frac{x}{x}$ at $x=0$ be $1$ or undefined, since without reducing it, you'd divide by $0$. I know the equation can simplify to $y=1$, but I thought…
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minimum number of times to change tyres.

I saw this brain teaser. Suppose, we travel 1000 miles on a tricycle and we have 5 tyres, then how many times do we need to stop to change tyres so that each of the tyres travelled the same distance? Here is a solution: After 400 miles change the…
Lost1
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Solving large multiplications in my head

What would be the best approach to solve 73 x 42 in my head? I started with 70 x 40 and then 3 x 40 and combined, but at this point I forgot what I had done and ended up getting lost and not figuring it out. Is there a good method for solving…
Jacob Raccuia
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How do you calculate the average number of lands in your hand in a game of MTG?

(This is actually a question and a half; Please tell me if this should be done otherwise) I have a magic deck of 60 cards. Some of them (say 25) are lands. The first card I draw has a 25/60 chance of being a land. If it is, the next card has a 24/59…