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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Math puzzle - Help with degenerate cases?

Here is the original problem: Given the following equalities and the values for $v,x,y\in \mathbb{R}$: $$\begin{matrix}v^2 = w(w-2x)(w-2y)(w-2z) & (1) \\ w=x+y+z & (2)\end{matrix}$$ Find all values for $z\in \mathbb{R}$. I will put my solution in…
SlipEternal
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Make a formula that gets a value and outputs another one

Invent a formula that asks for an input value and outputs a different value based on the input. The minimum input is 140, maximum input is 600. Here is some data that the formula should be based on. 140 input = 0.03 output 200 input = 0.42…
Gwapo
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Balls and scales (generalization)

A classical brain teaser is : You have twelve balls identical in size and appearance but one ball is an odd weight (could be either light or heavy). You have a set of balance scales. How many steps are necessary to identify the odd ball and to say…
Ernest
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How to solve this algorithmic puzzle?

For fixed integers $T\geq G>1$, we say a list $[a_1, a_2,\cdots, a_n]$ is normal if every consecutive sublist $[a_i, a_{i+1}, \cdots a_{i+T-1}]$ of length $T$ has less than $G$ maximal elements. Given a list $[a_1, a_2,\cdots, a_n]$ of $N$ numbers…
user1907531
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Calculating the diameter of planets when sun's diameter is scaled down to 50px

I am creating a scale model of the solar system for a personal website project and I am now stuck with the basics math for it. I have been banging my head against the wall trying to get things right but nothing beats being so poor at math. So, all…
Deepak Kamat
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Sophia washes pots in 30 minutes. Her mother takes 15 minutes to wash them. How much time will it take if they wash them together?

Sophia washes pots in 30 minutes. Her mother takes 15 minutes to wash same amount of them. How much time will it take if they wash those dishes together?
Zaif Senpai
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How many percent of the three digit numbers belong to the set $S = 3(70m+37n)$

I was crossing over the fact that some three digit (0-9) numbers can be expressed with the equation: $(n+2m)*10^2 + (n+m)*10^1 + n*10^0 = 3(70m+37n)$ But how would you determine, how many percents of the all three digit numbers from 000 to 999 can…
MarkokraM
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The intergalactic math problem?

Let's say that humans find a habitable planet 100 light years away and begin to build a ship that goes in the speed of light to get there. they fix hibernation pods in the ship so that humans could reach the planet without aging. while the ship is…
Kunal Mehta
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The nature of $(4x^3+6x^2+4x+1)^k$

I am trying to identify the mathematical properties of this polynomial $(4x^3+6x^2+4x+1)^k$. Most of all I’ve been attempting to describe an actual relationship to binomial coefficients, such as binomial$(4,n)^k$, and it’s very nature itself. How…
Mike Moye
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The License Plate Game

Premise: So, my father came up with a game where you would look at a 4-digit license plate make 2 pairs of numbers that were made from 2 of the digits from the license plate and were Identical Odd Numbers. Some example games may be: $$ …
user408996
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Calculating right time in clock angle problem

A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 10 p.m. on 4th day? I am completely messed up in this question. Can anyone please explain it with each step.
nban
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Math equation/formula to get quarter based on custom fiscal year end

Given the calendar year end, which is Dec, we know that Quarter 1 is Jan - Mar, Quarter 2 is Apr - Jun, Quarter 3 is Jul - Sep and Quarter 4 is Oct - Dec. My question is, is there a formula to get the correct quarter given the Year End (i.e. Apr…
David.L
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Prove $\frac{x^a-1}{x-1}$ is an element of the whole number set

If $x$ and $a$ are elements of the whole number set. Prove that $\frac{x^a-1}{x-1}$ is also an element of the whole number set.
Aspwil
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Solving for $f$

How should i solve expressions in $f$? $$ f(f(x))=e^x $$ or: $$ f(f(x+1)+1)=x $$ Series, expansions, discretizations, CAS, whatever? My normal approach is useless here...
Brethlosze
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Simple trading profit-loss problem

A man sells three articles A, B and C and gains 10% on A, 20% on B and looses 10% on C. He breaks even when combined selling prices of A and C are considered. He gains 5% when combined prices of B and C are considered. What is his net loss or gain…
Capcom
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