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
1
vote
0 answers

Space-Efficient Gear Shifting

The rules are as following: 1.Each gear has a width of 1 2.There are two shafts that have a fixed distance d between them 3.To change speeds, you can only slide one of the shafts to make gears of different sizes mesh together 4.Two gears can only…
Xiangyu Chen
  • 644
1
vote
2 answers

Guitar Pattern Question (Major Thirds Tuning)

Frets (1-4) . . . . . . . . . . . . . . . . Hey everybody. The four dots above are the four frets (vertical) and four strings (horizontal) of the imaginary guitar (sorry I'm not good at giving visual help). Here I'm…
pizzaking
  • 63
1
vote
0 answers

Understanding Benford's Law

I'm trying to wrap my mind around Benford's Law. According to wikipedia Benford's law applies in many "naturally occurring collections of numbers." It "applies to a wide variety of data sets, including electricity bills, street addresses, stock…
B flat
  • 792
  • 1
  • 6
  • 17
1
vote
3 answers

Passing Shillings

I am trying to solve one of Carroll's pillow problems, but even with the solution I can't really graps it. The problem is as follow Some men sat in a circle, so that each had 2 neighbours; and each had a certain number of shillings. The first…
Jorgel
  • 113
1
vote
1 answer

Swapping hands in a generalized clock

Consider a generalized clock, where the minute hand goes n times as fast as the hour hand, where n is a positive integer. The standard clock has n=12 (sometimes n=24). As which times can swapping the hour and minute hands result in a legal time? In…
marty cohen
  • 107,799
1
vote
1 answer

Two numbers that multiply to a product that contains the original digits

Recently I found an interesting combination of factors that forms a product that contains the original digits from those factors, as presented below: $$86 * 8 = 688.$$ Is there a name for these types of factors and products or is this just a…
MateoC
  • 11
1
vote
1 answer

Is there a function with random humps?

Is there an $(1)$ infinitely differentiable function that $(2)$ crosses the $x$-axis at and only at every integer where $(3)$ the pattern of the humps' sign is computable but not only by looking at whether every other hump is positive or…
Jacob Claassen
  • 868
  • 1
  • 8
  • 19
1
vote
1 answer

Knowing the time of arrival to point X

I have a bus that does A-------X------------------------B it goes at 10 hours from A, having: Speed at A sA = 10 m/s constant acceleration a = -0,5 m/s2 At what hour it will be at X, knowing the distance AX dAX = 50m ?
serhio
  • 129
1
vote
1 answer

Lemonade, Sandwiches, and Biscuits

Here is the example case. You might recognize this to be from Lewis Carroll's "A Tangled Tale". If you're already familiar, you can scroll down to the question. Example Given that one glass of lemonade, 3 sandwiches, and 7 biscuits cost \$14 and…
miles
  • 205
  • 2
  • 6
1
vote
1 answer

Diversity index between 0 and 1 for different proportions

I would like to come up with a measure of how diverse the population is. I have 3 groups of people: White, Black, Chinese. Let $\pi_i$ denote the proportions of the total population e.g.…
GRS
  • 2,495
1
vote
5 answers

The Collatz Conjecture

I was discussing the Collatz Conjecture with a friend of mine who's an engineer and a physics nut, and he made an interesting point. So I'll just assume we all know about choosing a positive integer n and then applying 3 n+1 to an odd integer and…
TheEighthMan
  • 27
1
vote
1 answer

Finding minimum given constraints

120 students enter a contest. The contest have 5 questions. It is known that for questions 1-5, 96, 83, 74, 66, 35 have scored respectively. If a student can win an award if he or she scored at least 3 times, what is the minimum number of students…
user122049
  • 1,632
1
vote
1 answer

Unique representation of reals by (infinite) application of the (+,-,/,*,^) operations to elements of $\mathbb Q$?

There are many ways to express $\pi$ by infinite application of some simple operation (+,-,/,*,^) . Is there a method that represents all real numbers uniquely? By method, I mean a restriction to certain operations applied in a certain way, such…
val11
  • 323
1
vote
3 answers

Does this set contain all real numbers between the $a$ and $b$?

If we define a set with $2$ elements in it $S=\{a,b\}$ and a variable "density" $d = 1$ here. Then if we continue to expand the set with more elements relative to variable $d$ arithmetically, in such a way that: $$(d=2) \to S= \{a,…
Vepir
  • 12,516
1
vote
1 answer

deviation from average on a scale from 1 to 100 (personality test)

Note: Im not sure Im using the proper "Math" term here in deviation, it is what google translate gives me for the dutch "Afwijking" I got this question from my father in law who took a personality test to take a look at how his scores were…
Durielblood
  • 113
1 2 3
…
35 36