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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Shannon number upper and lower bounds

What are the best proved upper and lower bounds for the Shannon number, i.e. number of possible positions of chess? Is the upper bound 7728772977965919677164873487685453137329736522 given in http://homepages.cwi.nl/~tromp/chess/chess.html generally…
chessmath
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What is the Smallest Integer $N$ Where Reversing the Digits Makes $3N$?

What is the smallest positive integer N such that the integer formed by reversing the digits of N is triple N? (Does such an integer even exist? If not, then for what multiplier for $N$ will such an integer exist?) Here are my thoughts so far:…
feralin
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What is the sum of the numbers in the shaded circles?

Each of the 6 circles contains a different counting number. The sum of all 6 numbers is 21.The sum of the 3 numbers along each side of the triangle is shown in the diagram. so What is the sum of the numbers in the shaded circles? Note that…
Mazdak
  • 367
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Determing the number of possible March Madness brackets

Is there a simple combinatorial explanation to derive the total number of march madness brackets? Would it be $2*(2^{16}*2^{8}*2^{4}*2^{2}*2)^{2}$ where the final squared takes into account both halves of the bracket?
lord12
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What's the least number of car parked?

In a car park, there are 2 white car for every 3 blue cars and for every 2 blue cars there are 5 silver cars. What is the least number of cars in the park? I am a bit confused about my approach to the question, according to my…
Saharsh
  • 854
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How can $1 + 2 + 3 + ... = -\frac{1}{12}$?

Recently there's been a lot of buzz created by this video http://www.youtube.com/watch?v=w-I6XTVZXww which states and goes on to prove $$1 + 2 + 3 + ... = -\frac{1}{12} $$ I know that the above series is actually $\zeta(-1)$ where $\zeta$ is the…
ajay
  • 1,165
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Maximum sum of the number of saturdays and sundays in a leap year

Question is to find maximum sum of the number of Saturdays and Sundays in a leap year... I do not have much to show off but I guess in a leap year there would be maximum of $53$ Saturdays/$53$ Sundays but i am not sure if it is possible to have…
user87543
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Can we make rectangle from this parts?

I have next problem: Can we using all parts from picture (every part exactly one time) to make rectangle? I was thinking like: we have $20$ small square, so we have three possibility: $1 \times 20$, $2 \times 10$ and $4 \times 5$. I can see clearly…
user110822
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What points do have three points with minimal distance on $x^2$?

Suppose you have a function $f: \mathbb{R} \rightarrow \mathbb{R}$ and a Point $P = (x,y) \in \mathbb{R}^2$. Now you want to find all $x_1, \dots, x_n$ such that $$\forall \tilde x \in \mathbb{R} \setminus \{x_1, \dots, x_n\}: d(P, (x_1, f(x_1))) =…
Martin Thoma
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given a positive integer $n\geq 2$, we have a positive integer $m$ such that $m+2,m+3,\dots m+n$ are composite. (TIFR exam $2012$)

Question is to prove that : given a positive integer $n\geq 2$, we have a positive integer $m$ such that $m+2,m+3,\dots m+n$ are composite. I tried checking for small numbers to see if there is any pattern... for $n=3$, i have $m=6$ with …
user87543
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Question about Horses

For P(n) being the assertion that in every set of n horses, all horses have the same color: P (n) ⇒ P (n + 1), when n > 1. How do I prove this problem, can someone give me explanation or a headstart?
user96778
  • 21
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How determine largest reflected number

I was trying to determine maximum number from list of given integer in problem 8 here (page 5). So as you see, there are 5 written numbers on paper, and on the wall there is a hanging mirror. We should determine which row contains the largest…
dato datuashvili
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How to measure bias in a subgroup of people

I have a small fun problem that I gave myself to represent mathematically, but I got stuck very quickly. Suppose there is a group of people (named A, B, C, D, E, F and G). Every week they meet: every person speaks then nominates the next person to…
gigio
  • 21
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Which recreational math problems could qualify for a Fields Medal during the last 10 years?

Exploring the realm of recreational mathematics, I am intrigued by the notion that problems within this playful domain could serve as a catalyst for significant mathematical development. I am particularly curious to know if any mathematicians have…
Néstor Briceño Estepa
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Alligators and Creepy Crawlers

I got this math question wrong, but I'm not exactly sure why. Here's the question: If all alligators are ferocious creatures and some creepy crawlers are alligators, which statement(s) must be true? I. All alligators are creepy crawlers. II.…
Andrew Hu
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