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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Proving you *can't* make $2011$ out of $1,2,3,4$: nice twist on the usual

An undergraduate was telling me about a puzzle he'd found: the idea was to make $2011$ out of the numbers $1, 2, 3, 4, \ldots, n$ with the following rules/constraints: the numbers must stay in order, and you can only use $+$, $-$, $\times$, $/$, ^…
Kevin Buzzard
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Turning coins on a chessboard

Alice and Bob are playing a game on a $n \times n$ chessboard. Alice puts coins on each square; she may choose to put any one of them heads up or tails up. Then Bob may perform any number of moves, where a move is to turn all coins in a single row…
mau
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Using Overpowered Theorems to Solve Easy Problems

I thought it would be interesting to start a thread about using overpowered theorems to solve easy problems. Two examples come to mind. Post your favorite example of problem and solution! 1). $\sqrt[3]{2}$ is irrational. Proof: Suppose $\sqrt[3]{2}…
mathworker21
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For which number does multiplying it by 99 add a 1 to each end of its decimal representation?

This was asked by my maths lecturer a couple of years ago and ive been wracking my brains ever since: Find a number that, when multiplied by 99 will give the original number but with a 1 at the beginning and a 1 at the end. For example:…
Tom
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Interesting Math for 3-graders

I'm supposed to give a 30 minutes math lecture tomorrow at my 3-grade daughter's class. Can you give me some ideas of mathemathical puzzles, riddles, facts etc. that would interest kids at this age? I'll go first - Gauss' formula for the sum of an…
Amihai Zivan
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Is 39 moves the longest a chess game can go moving only pawns?

I've thought of a few different ways a chess game could go on moving only pawns, but I've only counted moves in one scenario: Both White and Black take 16 moves to line their pawns at the middle of the board. With a series of orderly captures in 8…
Robert Soupe
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Choosing points in fractions of the unit interval

How long a series of points in (0,1) can be chosen such that the first two are in different halves, the first three are in different thirds, ... the first $n$ are in different $n^{\text{th}}$s? My first try of…
Ross Millikan
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Contemporary Mathematical Columns in Magazines

In good old days, Scientific American was host to some legendary mathematical (and computer science) oriented columns that inspired generations of scientists and engineers. Douglas Hofstadter, Martin Gardner, A. K. Dewdney... just to name a…
Hugo Sereno Ferreira
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$\square\square\times\square =\square\square\square =\square\times\square\square\,\,\,$ fill blanks with distinct numbers from$\{1,2,3,4,5,6,7,8,9\}$

Fill in the blanks of: $$\square \;\square \times \square = \square \; \square \;\square =\square \times \square \;\square $$ With distinct numbers from the set $\{1,2,3,4,5,6,7,8,9\}$. I was able to do it by trial-and-error, but I am looking for…
maths lover
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Show there is an uncut square lying in a larger square cut by lines

I found this problem on Keith Ball's blog sometime ago but I've never really worked it out. Show that if a square is cut by two lines (shown above in green) then there is an uncut square at least one third as large (shown in red) lying inside…
E.Lim
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How many trees in a forest?

Some time ago I met a forester. He told that there are only larches and spruces in his forest. He also said that there are exactly $10$ spruces at the distance of exactly 1 km from each larch. Next, he argued that there are more larches than…
Martin Gales
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Number of lines to connect $n \times n$ dots

The following is a popular riddle: Draw a $3 \times 3$ grid, and connect all the dots using only $4$ straight consecutive lines. The solution is to think outside of the box and do the following: My question is, what is the minimal number of…
Krijn
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"Liar functions": is this a known concept?

While reading this comment and thinking about how you could change the functions without convergence (because the Lebesgue integral doesn't care about changes at countably many places), I just arrived at a concept which could be called "liar…
celtschk
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Represent $1729$ using four fours only.

I keep trying Four fours puzzle for various numbers, i.e. express a number using four fours and only four fours along with any mathematical operation. Today, I was thinking for Ramanujan number, i.e. $1729=10^3+9^3=12^3+1^3$. I think using…
Departed
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Two players placing coins on a round table with the goal of making the last move

I came across this riddle during a job interview and thought it was worth sharing with the community as I thought it was clever: Suppose you are sitting at a perfectly round table with an adversary about to play a game. Next to each of you is an…
Chris
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