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
2
votes
1 answer

Where does this picture come from (or what does it illustrate)?

Sorry if this doesn't belong here, but I do think this is math-related. I stumbled upon a interesting looking picture a while ago (I think it was either on Stackexchange or Reddit), and I had saved it to my desktop. I recall that it had some…
Natash1
  • 1,379
2
votes
1 answer

Runs of 2s in a rep digit sequence

Today I asked a question about a particular sequence of numbers on code-golf.se. This $n$th term of the sequence is defined as ... the length of the longest rep-digit representation of $n$ in any base A rep-digit, is any number where all the…
Sriotchilism O'Zaic
  • 2,228
2
votes
2 answers

One stick and Pythagoras

I am strugling with a question: How can you design a right-angled triangle if you want a certain perimeter? let's say I have a 1 meter stick and I want to turn it into a right-angled triangle. Is there only 1 solution? Thanks!
Jesper Jelle Albinus
  • 21
2
votes
2 answers

Expansion of $(1+x)^{-n}$ when x is not less than 1.

I was told that binomial expansion of $(1+x)^{-n}=1-\dfrac{n}{1!}(x)+\dfrac{n(n+1)}{2!}x^2\cdots$ is only valid when $|x|\lt1$. But what happens when $|x|$ is greater than 1 ($|x|\geq1$) ? Why it is not defined for x greater than or equal to 1? I…
Fawad
  • 2,034
2
votes
1 answer

Search for the nth 3d pentagonal numbers(challenge)

There are square numbers, we can imagine these as a square of dots Squ(n) $= n^2$ There are triangle numbers with we can imagine as a triangle of dots tri(n) $=\frac{n(n+1)}{2}$ There are pentagonal numbers we can imgaine these as a pentagon of…
Aspwil
  • 105
2
votes
1 answer

Prove that $\sum\limits_{i=1}^{n} \frac{1}{x_i} < \frac{15}{8}$

I came across the following recreational problem and am not sure if I did it right: Let $x_1, \ldots, x_n$ be odd numbers with a prime divisor not greater than 5. Prove that it must hold that $$\sum\limits_{i=1}^{n} \frac{1}{x_i} < \frac{15}{8}$$…
Taufi
  • 1,095
2
votes
5 answers

Speechless mathematical proofs.

Do you have proofs without word? Your proofs are not necessary has zero word, you may add a bit explanations. As an example, I has a "Speechless proof" for $$\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+...=\frac{1}{3}$$ I welcome all aspects of…
JSCB
  • 13,456
  • 15
  • 59
  • 123
2
votes
0 answers

Proof that 0.1011011101111... is irrational

I know that any rational number has a repeating decimal and therefore the number 0.1011011101111... cannot be rational, however, I don't know the proof of that claim--and besides, I'm curious if there is some particularly easy proof in the case of…
Addem
  • 5,656
2
votes
3 answers

Examples of unexpected names of concepts in mathematics

I was wondering around wikipedia and I found two concepts called "Monstrous moonshine" i.e. In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the…
Scavenger23
  • 1,177
  • 8
  • 23
2
votes
0 answers

Tilting sealed drums for fun

A sealed cylindrical drum of radius r is filled with 9% of water. Now if the drum is tilted to rest on its side, show that the fraction of the curved surface area (not counting the flat sides) that will be under is water is less than 1/12 . What…
Mateen Ulhaq
  • 1,211
2
votes
0 answers

Casino Bonus Requires 35 Times Wagering Before Withdrawal, Worth It?

I took advantage of a free slot machine $50$ spin bonus (no deposit required) on a casino site. I won $£50$ and managed to turn that into $£600$ (so I have $£600$ in my bonus balance). In order to turn the bonus into cash, you must wager at least…
Desmoz
  • 362
2
votes
3 answers

Natural number divisible by $42$?

There is a natural number divisible by $42$. The sum of digits which do not take part in the written number is $25$. Prove that there are two identical numerals in the natural number.
McLinux
  • 421
2
votes
4 answers

Finding the correct time

At a certain time between 3pm and 4pm, the hour and the minute hands are at equal angles from the 6 mark, what time will it be exactly? My approach is at the time t(minutes) the following should hold 180 - 0.5t = 6t -180 Thus we get the time in…
uzumaki
  • 621
2
votes
1 answer

Guess colour of hats from neighbors

Four people stand in a circle, each wearing a hat which is one of $n$ colours. Each person can see the two neighbours. They must simultaneously guess the colour of their own hat. If at least one of them guesses correctly, they all win. For which $n$…
pi66
  • 7,164
2
votes
3 answers

Can 2 + 2 ≈ 5 be true?

I was wondering a little, about how to proof that 2+2 =5 And here I am: 2.4 + 2.4 = 4.8 If we approximated numbers in each side individually then : 2 + 2 ≈ 5 I know this may not be right, but I don't know why it's wrong.
mohamedrashad
  • 23
1 2 3
…
35 36