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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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Base 12 Versus Base 16

I'm not good when it comes to math, so forgive me. I'm doing a personal study of is there a better base number for our culture to use? I have to consider factors like: the number of digits to write, ability to count visually(like using fingers),…
Xarcell
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Jed does pushups every week day. On Monday he does 7. He doubles his average every day he works out. How many push ups does he do next Monday?

Jed does pushups every week day. On Monday he does $7.$ He doubles his average every day he works out. How many pushups does he do next Monday?
Plastic Fork
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What is the easiest and fastest way to produce a uniformly distributed random number between 0 and 9 off the cuff?

Let’s assume, you are in a rush and you need a random number: What is the best way to produce a high-quality, uniformly distributed random integer number between 0 and 9, ideally using only mental math or, less ideally, tools that are commonly…
Lenar Hoyt
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Generalizing a number puzzle: maximizing the product of two numbers formed from nine digits

Maximize :: $A = B \times C$ asks for two decimal numbers which, combined, use the digits from $1$ through $9$ exactly once, and which have the greatest possible product. (Actually, it asks for the product, but I want the factors). kba's answer to…
dfeuer
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How many sepak takraw balls with distinct patterns can we make?

Sepak takraw is a sport native to the Malay-Thai Peninsula. A few days ago, a friend of mine taught me how to make a sepak takraw ball. The ball is related mathematically to a $32$-face semi-regular polyhedron, known as a truncated icosahedron. We…
mathlove
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Can you find nice parameters for a point that has two closest points on a quadratic function?

When you have a quadratic function $$f(x) = a x^2 + bx + c$$ and a point $$P = (x_p,y_p)$$ you can find one or two points on the graph of $f$ that have minimum (euclidean) distance $$d_{P,f}(x) = \sqrt{(x-x_p)^2 + (f(x)-y_p)^2}$$ Example When you…
Martin Thoma
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Swap two integers in different ways

This is a famous rudimentary problem : how to use mathematical operations (not any other temporary variable or storage) to swap two integers A and B. The most well-known way is the following: A = A + B B = A - B A = A - B What are some of the…
ND_27
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Converting dot producto to set of arithmetic mean differences?

Ok so I am reading a book on linear algebra ( Gilbert Strang to be specific) and I am on second problem set, challenge problem, problem 29. In solutions it appears that the author states that: $$x\cdot y=xz+yz+xy=(1/2)(x+y+z)^2 - (1/2)(x^2 + y^2 +…
Vanio Begic
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Why these exact values?

In Mathematica I have In[181]:= FullSimplify[ArcSin[10^(1/2)] == (Pi/2 - ArcSinh[3] I)] Out[181]= True In[206]:= FullSimplify[ArcSin[100^(1/3)] == (Pi/2 - ArcCosh[10^(2/3)] I)] Out[206]= True In[198]:= FullSimplify[ArcSin[1000^(1/4)] == (Pi/2 -…
Marvin Ray Burns
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Stuck on a basic thinking question

Stewart and Michael have arranged to meet. Michael is about to set off on his bicycle, and at the same time Stewart is going to run to meet him. Michael can cycle at a steady 20 kilometres per hour and Stewart can run at a steady 12 kilometres per…
salman
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How many multiples of 3 are between 10 and 100? (SAT math question)

In the figure above, circular region A represents all integers from 10 to 100, inclusive; circular region B represents all integers that are multiples of 3; and circular region C represents all squares of integers. How many numbers are represented…
anita
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What are all possible numbers gotten by an digit-exchange operation?

A friend of mine taught me a number game. Supposting that $a_na_{n-1}\cdots a_1$, which satisfies $a_n\gt a_1$, is a natural $n$-digit number with decimal representation, let's consider the following operations : 1. $a_na_{n-1}\cdots…
mathlove
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compare which two cube is the same

I am solving following problem: The problem states that on figure 1 there is shown a cube with three facets on which there is drawn three section(length). This cube was put on other facet and turned such that there is also shown these three …
dato datuashvili
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Find the largest prime factor.

Is there a method to find the largest prime factor of $2^{2024} + 2^{2023} + 2^{2022} + 2^{2021}$? Like I know that's the same as $15 * 2^{2021}$ but where do I go from here?
Lxwrxncx
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Show me where I have made a mistake in interpreting or solving this number puzzle

The following number puzzle was published in the Sunday Times on 25th August this year. It is credited to Danny Roth. George and Martha have a book of puzzles numbered from 1 to 30. The solutions are also numbered from 1 to 30, but a solution…
Hammerite
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