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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What can be the value of $m$ in following equation

During calculations I got this step $$(e^m/((m+1)^{m+1}) )^{3n/4} = 1/2^n$$ I want the value of m here??
Chandrashekhar Garkar
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Prove problem of Mathematical Reasoning

The gcd of two integers $a$ and $b$ (both not zero) can be described as the smallest positive integer of the form $am+bn$, where $m,n \in \Bbb Z$. Prove that every positive $x$ of the the form $x=am+bn (m,n \in \Bbb Z)$ is an integral multiple of…
Hao
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Man walking along a circle falling in a ditch.

Consider a circle as in the figure. It has a small ditch of width $L$. A man is walking around the circle with step length $\alpha$ (measured along the circumference). $\alpha$ is irrational. We need to prove that sooner or later he will step into…
QED
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Given any equation, can we definitively determine in finite time whether or not this equation can be solved to give a symbolic answer?

Given any equation, can we definitively determine in finite time whether or not this equation is solvable by non-numerical methods to give a symbolic answer? It is trivial to show that there exist equations which is provable to have a symbolic…
Thomas Eastgate
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Please make expressions equal to 6 using exactly four 4s

Background: I am the source. I created this puzzle. This problem belongs in the Mathematical Puzzling section. If this is not the correct subforum, then I am asking it to be moved. People have already begun answering with solutions, and it…
Olive Stemforn
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Weighted Average Rate with multiple variables

Easy - Situation 1. I have an existing loan with $\$200\;000$ balance and a $4.00\%$ interest rate. I take out an additional $\$200\;000$ loan on the same property and current rates are at $8.00\%$. The lender blends the rates to $6.00\%$. My limit…
DiabloMonkey
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Successor Function in high numbers

Recently, I tried creating a Peano-based googology model. I started with 10^3003, which I understand is named a millillion. I then defined a millillillion - or, for short, a thousand 2ill (there are 2 ills, because mille means thousand) - as…
Mark Smith
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$N^2$-ball Bingo Game with $N \times N$ Bingo Card Theorem

In this modified version of bingo game, there are total of $n^2$ bingo balls, half of the bingo balls will be randomly rolled out (in the case of odd number of balls, round up to nearest integer). What are the maximum possible of bingo lines…
PowerPii
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Moving average on a list of numbers while keeping same total value

I need to replace a list of numbers, [1,0,3,2,1,4,1,2] for instance, by the moving average with a window of 3. The second element, 0 in this case, should become (1+0+3)/3. The problem I have is that I want to keep the new total the same as the…
maRmat
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Finding Date Conversion Rate Logic

I need your help to complete this sequence, I have to find the right logic to go from one date to another and thus find what the rate corresponds to. For now, all I could find, and which seems pretty obvious, is the number of years between the two…
Bo Halim
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Let S be the set of all infinitely differentiable functions...

Let S be the set of all infinitely differentiable functions whose domain and range are the real number. Let $S_1, S_2, S_3, $ and $S_4$ be the fours subsets of the S defined below: $S_1$ = The set of infinity differentiable functions $f(x)$ such…
Kevin Perez
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A) Find Intersection Omega and prove your conjecture. Let Omega ={An: N=1,2,3,...}, where An={0, n, n+1, n+2...}

Let Omega ={An: N=1,2,3,...}, where An={0, n, n+1, n+2...} A) Find Intersection Omega and prove your conjecture. B) Find Union Omega and prove your conjecture. I'm completely lost on these types of questions. I have reached out to our group chat for…
Casey Sharp
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How can you represent the maximum value of two bytes as 255×256+255

The computer uses base $256$ instead of base $10$. Two adjacent bytes can represent numbers between $0$ and $255 \times 256 + 255 = 65535 = 2^{16}−1$, inclusive. I understand how a byte is $8$ bits and $0$ is the starting point, so two bytes would…
Wildblue09
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Making regular sequences from a not necessarily regular sequence, but how many unique reqular sequences can we actually make?

Making regular sequences from a not necessarily regular sequence, but how many unique reqular sequences can we actually make? TL;DR: I thought of a way to make up to $2^{N-1}$ regular$^1$ sequences from a not necessarily regular sequence $S$ of…
joseville
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Where is the flaw in this logical argument?

Let's say Adam has 10 apples. If Beth asks Adam how many apples Adam has, and Adam replies I have 7 apples, would that be a lie or a true statement? In defense of Adam: It is true that he has 7 apples, however he also has an 8th, 9th, and 10th apple…
Y Timen
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