# Questions tagged [recreational-mathematics]

Mathematics done just for fun, often disjoint from typical school mathematics curriculum. Also see the [puzzle] and [contest-math] tags.

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### Puzzle: Calculate amount of combinations of "houses" [closed]

I've found this enigma in a french book and I've tried using combinatorics to find the answer but I've been unsuccessful, could you help me out? Here's what's given: "A child wants to build "...
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### Doubt about Gardner' solution to bug chase problem

A famous Martin Gardner problem goes something like this. Four bugs are placed on the corners of a 10-inch side square. Each bug is looking at the bug to its right and starts to walk towards it. ...
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### Calculating damage per second that can stack and have stack limit, with variety of durations

Lets say, a plane attack a ship once every 12.80 seconds, each attack throw 6 bombs, and each bomb have 25% chance of giving the ship 1 stack of fire. When the ship get 1 stack of fire, it will deal ...
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### At any given point in time two players have finished the same number of games

I am reading the following problem, which falls under the Pigeonhole principle. A chess tournament has $n$ participants and any two players play one game against each other. Then it is true that at ...
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### How to invert $\binom{9}{x} \binom{x}{\lfloor \frac{x}{2} \rfloor} = \sum_{k=0}^{3} f(x,k) \: 2^k$ in relation to Tic-Tac-Toe?

"Tic-Tac-Toe" is a game played on a 3x3 grid where 2 players alternate taking turns placing tokens (X's and O's) onto the grid. The game is completed when one player has reached 3 of their ...
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### Does Fermat's Last Theorem imply $\sqrt{2} \not \in \mathbb{Q}$?

A well-known overkill proof of the irrationality of $2^{1/n}$ ($n \geqslant 3$ an integer) using Fermat's Last Theorem goes as follows: If $2^{1/n} = a/b$, then $2b^n = b^n + b^n = a^n$, which ...
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### How to draw the function $y'(x) = y(x)(y(x)-1)^{1/3}$ qualitatively?

Let $k \in R$, consider the following Cauchy problem $$y'(x) = y(x)(y(x)-1)^{1/3}$$ $$y(0) = k$$ To draw the graph of solutions, defining the domain, studying the monotonicity, the convexity, and ...
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### How is the diagonal constraint in lattice path needed for the Catalan proofs?

I have been reading about the Catalan numbers and how they are they appear in many problems such as: lattice paths valid pair of parenthesis mountains with up/downstrokes non-crossing handshakes ...
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### Formula to maintain distance along the x-axis between an outer object and an inner object while scaling

Formula to maintain distance along the x-axis between an outer object and an inner object while scaling: ...
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### Group of 9 people, with(out) 3 people who all know each other

Problem: In a group of nine people, one person knows two of the others, two people each know four others, four each know five others, and the remaining two each know six others. Show that there are ...
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1 vote
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### Definition of aperiodic tiling

I think I got confused with the definition of aperiodic tiling. Look at the following example: First, try to find a "1-dimensional aperiodic tiling". Start with the string 0, then make the ...
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### Is there a simple test for divisibility by sixteen in base-twelve?

I am investigating math in the dozenal (a.k.a. duodecimal, base-twelve) system. As part of this, I am compiling a list of tests for divisibility. (All numbers in this post are dozenal, not decimal, ...
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### A math logic problem [duplicate]

Say there are 12 people on an island, 11 weigh the same. One is either lighter or heavier. There's a beam balance to measure the weights. Is it possible to find the heavier OR lighter person in only 3 ...
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### Mathematics hiding in plain sight

What are some basic math facts (say, secondary or early undergraduate level) that somehow went unnoticed by you for a long time, and when you realized they made you wonder how you could have missed ...
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### Finding all numbers such that this algorithm calculates their square

A relative of mine found an algorithm on TikTok that could supposedly calculate the square of any two digit number. The number 35 was used as an example, so I shall use it to explain how it works: ... A Texas Hold'em poker tournament has $1557$ players, in $9$ distinct positions at $173$ tables. Each table has a standard $52$ card deck, and each player is dealt $2$ cards. Hands are considered "...
A psychic calls everyone on a list of $275$ sports bettors with tips about who will win the "hard-to-predict" games in the first round of the NCAA "March Madness'' tournament. This ...