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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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What is the height of overflow over vessel edge?

Hello, Consider a flow (at an x flow rate of incompressible fluid) flowing into a vessel (let's assume it's a round vessel with diameter d). How to calculate the height of overflow,h, over the edge of the vessel? I know $flowrate_{In}$ =…
GRANZER
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A question I got from an 8 years old kid:

I got this one from an 8 old kid who got this at school Can you get the number in the right by using the numbers on the left with the rules: Each number should be used 1 time exactly, The allowed operations are: $(,),+,-,\cdot,/$ A solved exercise…
user135172
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Calculating A Retrograde Of Mercury - Total Beginner Question

I am a total beginner to doing this kind of math, so there is a mean learning curve. There is need to calculate the number of seconds from when mercury is direct to the next direct phase. My thoughts about doing this: speed of mercury =…
Misfit
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Show that the numbers 1, 2, 3, ..., 16 can be arranged in a line so that the sum of any of two neighbors is a square.

Ex.: 8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9, 16 The sums are: 9, 16, 25, 16, ... In fact I want to know for which numbers N the numbers 1, 2, 3, ..., N has this property. Maybe the sum not being a square but a cube or k-th power, or maybe…
lucas
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Freeing the trapped knight

The trapped knight problem is as follows. Place all natural numbers (starting with 1) in a spiral on an infinite square grid. A knight begins in the cell labeled 1. Each turn it jumps (in an L-shape) to an unvisited cell with the lowest number. It…
Dmitry Kamenetsky
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How to calculate this limit, in terms of $a, b, k, ..$?

$$f(0) = a \\ f(n+1) = f(n) + f(n-1) \\ g(0) = b \\ g(n+1) = g(n) + g(n-1)$$ $$ \lim_{n \to \infty} {{f(n+k)} \over {g(n)}}$$ where $a, b, n, k \in \mathbb Z$
carlos
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Five digit re-write game

In the habit of factoring numbers, a notebook I bought had a five digit item number $77076$, which factors as $2^2 3^2 2141$, which may also be $9 \cdot 8564$, and in this form the count of digits is again five. (Repeated digits count separately).…
coffeemath
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Recreation math : Fill the box type problem with equal sum of row and column

Today I solve an interesting recreational math problem which took some time. First I will briefly explain the situation of the problem. Look above figure. (1) a,b,c,d,e,f,g,h,i,j are one of 1,2,3,4,5,6,7,8,9,10 (2) the sum of each row and…
phy_math
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Calculating population movement between countries... unsure what to tag this as

I apologize if this is a slightly vague question. Let's say that I have yearly data containing the amount of births, amount of deaths, and the total population in each of the 6 regions throughout the world. Let's assume that this data is…
tfr950
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If we were to locate another intelligent lifeform, how could we then estimate the total number of intelligent lifeforms in the galaxy?

Given the vast size of the Milky Way, it is unlikely that we are the only intelligent lifeform to be found within it. Given that we only have one data point (the Earth), we are forced to use a long series of guesses to estimate the number of other…
PhiNotPi
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What digit positions in a different base can be potentially altered given a change in a specific digit of current base

I am not a mathematician. I have some number $A_b$ which has a digit in a position $p$. That number can be written in another base as $V_d$ and it will have a range of digits $q_{start}$ – $q_{end}$ which hold (potentially added with other values)…
v010dya
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Provided the shape $(m, n)$ of an unknown matrix $A$, as well as the value of the matrix $(A^T A) * (A A^T)$, could you find the initial matrix $A$?

Problem Consider a matrix, $\mathbf{A}$, of shape $m \times n$. Now, let $\mathbf{A_1}$ equal the matrix multiplication of the transposition of $\mathbf{A}$, a.k.a. $\mathbf{A}^T$, by $\mathbf{A}$ itself. In addition, let $\mathbf{A_2}$ equal the…
Ryan Rudes
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how to solve for length of diagonal board between columns

I was watching a youtube video the other day and the guy was figuring out the length of a board needed to fit diagonally between two columns. He did it in an approximate way that worked fine, but it got me to thinking: how would one solve this…
Shaggoth
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Values of n(S) such that the gears can rotate at once

While watching YouTube videos, I came across a puzzle that had a pretty interesting solution and an underlying question behind it. Question: Let $S$ be a set of gears that are connected to form a ring such that $n(S)\geq0$, $n(S)\in N$. For some…
Darrell Tan
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complete the grid square

Here below is a challenge that circulated on internet. Complete the Square Grid! $$\begin{array}{|c|c|c|c|c|}\hline & & & 20 & 21 \\\hline & 6 & 5 & 4 & \\\hline 23 & 7 & 1 & 3 & \\\hline & 9 & 8 & 2 & \\\hline 25 & 24 & & & 22\\\hline…
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