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Questions tagged [recreational-mathematics]

Puzzles, curiosities, brain teasers and other mathematics done "just for fun".

0
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1answer
46 views

A math riddle involving sums of digits

When I was in highschool I became obsessed with this strange combination I discovered. I don't really know a lot about math but I've recently re-discovered it and believe I have found an answer, but ...
0
votes
1answer
32 views

How to guarantee entry into cave

Ali Baba is trying to enter a cave. At the entrance, there is a drum with four openings, in each of which there is a pot with a herring inside. The herring may be lying with its tail up or down. Ali ...
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0answers
37 views

Queens on a torus chessboard.

Consider a Torus chessboard $\mathbb T$ of dimension $8\times8 $. How much queens it is possible to put on in such a way that no one attacks another? (I assume we use the same rules of standard ...
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0answers
31 views

How big does a digital file has to be, to be faster to transport it physically than to transmit it over the internet? [on hold]

When internet speeds were very low this was a very relevant question, and it was even considered to use pigeons, nowadays is more of a simple math question. For you to copy a file from a computer to ...
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0answers
43 views

Network Connectivity Problem

Assume a network (a complete undirected graph) comprised of $N$ participants (vertices). Each person holds a different piece of information, unknown to all other members. The participants can ...
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0answers
29 views

Problem for elementary school -find letter a number such that - $SEND+MORE=MONEY$ [duplicate]

Problem: Find the number for every letter(different letter is a different number) such that this equality holds. $$SEND+MORE=MONEY$$ My solution: Because idea of this problem isn't to solve it's to ...
2
votes
1answer
56 views

How many half-squares can cover a square?

Let $I$ be a set of size $2n$. Given any subset $S\subset I$ of size $n$, we call $S^2=S\times S$ a half-square. Question: How many half-squares can cover the whole square $I^2=I\times I$? Denote ...
0
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1answer
17 views

What is this definition regarding the locker problem saying?

I am currently working on the famous "locker problem." For those unfamiliar with this problem, this question here does a great job of explaining what it's all about. My question today has to do ...
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0answers
12 views

On maximizing sum of fraction nominators after removing some fractions

I am looking for a formula to calculate something like the title (perhaps) suggests. I am having problem formulating my question rigorously so let me give the example. I have four fractions $\frac{a}{...
0
votes
1answer
37 views

Batting average

How would you interpret this problem? * Let $h$ and $n$ be the number of hits and number of at-bats after hitting the single, respectively. The answer to the problem suggests solving from the ...
2
votes
0answers
66 views

Integral of function $f(x)=\begin{cases} 1 & \text{if $x = 1$}\\ 0 & \text{otherwise} \end{cases}$ [closed]

Need to find the integral of the function $f$ where for $x\in\mathbb{R}$, $$f(x)=\begin{cases} 1 & \text{if $x = 1$}\\ 0 & \text{otherwise} \end{cases} $$ I think it's zero because $f(x)$ ...
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2answers
59 views

Finding a formula for a sequence or proving it is impossible [closed]

I tried to search for a formula that produces the following sequence: 35 49 55 65 77 85 91 95 115 Etc, a larger sequence is in the following link: https://pastebin.com/HDDHe7bz Or proving that such ...
2
votes
3answers
50 views

Why does this method for differentiating work? [duplicate]

Consider the function $$f(x)=x^x.$$ If I differentiate with respect to $x$ treating the exponent as a constant and then sum the derivative treating the base as a constant, I get \begin{align} f'(x)&...
2
votes
1answer
80 views

Probability 3 points are collinear

Given $n \ge 3$ points with real number coordinates, distributed randomly in a unit square, what is the probability $P$ that 3 points exist which are collinear? My reading of this answer to a similar ...
0
votes
2answers
37 views

How to know 2 unknown variables using 2 equations?

Trying to make my AI hit people. So I need a formula to know the time until my projectile will hit the target and also the direction the projectile should be shot at. Here is an example scenario. ...
0
votes
1answer
24 views

In a grid of convex polygons, what is the maximun number of adjacent neighbors a polygon could have?

Maybe is a dumb question, but I'm working in a procedural map generation system. Each map is composed by regions. I know for sure that each polygon is convex, because I'm using a Voronoi space ...
0
votes
0answers
28 views

How to mark a stack of cards to reduce the effort to find a specific card.

I have a pile of thick cards. The cards are thick, so I can make marks on their borders, to identify the card on the pile. I need to rapidly find the card with my name written on it (not written in ...
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2answers
36 views

How can I express this solution in terms of the error function?

If I have this expression: $$u(x,t) = \frac {U_o}{\pi} \int_{-\infty}^{\infty} \!\frac{\sin(\alpha) \cos(\alpha x) e^{-k\alpha^2 t}}{\alpha} \,d\alpha, $$ how can I rewrite it in terms of the error ...
1
vote
4answers
127 views

What is the probability that Fra wins?

Fra and Sam want to play a game. They have two classic coins Head-Tail. They flip the coins at the same time. If the result is $HH$, Fra wins. If the result is $HT$ (or $TH$), they flip again and ...
0
votes
1answer
52 views

Formula that predicts the location of moving enemy

A rocket that explodes not on impact, but explodes on a timer will be shot from myself to the enemy. The timer can only be inputted at the start of the shot. The rocket can only go straight and has a ...
5
votes
1answer
67 views

How could Bob help Alice

Suppose there’s a sequence $a$ of 0 or 1, that is long enough , eg $length(a)=2^n$, $n$ sufficiently big enough integer. Now Alice is to guess the content of $a$. If Alice knows nothing about $a$, in ...
6
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0answers
53 views

People's preferences assigning them to a group using Excel

I would love some assistance with the following problem. Each year for school camps we take the students preferences 1-6 of who they'd like to bunk in with for the week. We usually sort this out ...
1
vote
1answer
56 views

Point in a square

Suppose you have a random point inside a square and you set the point moving in a random direction. When the point hits a side of the square, it bounces off the side like a billiard ball, i.e. angle ...
2
votes
0answers
24 views

Simplify a weighted average with enumerations as weights

Could you help me simplifying the following expression: $$\forall l \ge 0, \forall n_1,n_2 \gt 0, \forall k_1 \in [[0,n_1l]],\forall k_2 \in [[0,n_2l]],$$ $$m_{l,n_1,n_2}(k_1,k_2) = \frac{\sum_{i=0}^l ...
2
votes
1answer
102 views

Billiard ball mental patients.

The Question: Suppose there are $n$ extremely paranoid, vulnerable mental patients at a hospital. Each day at the lunch hour, they move around like frictionless billiard balls of radius $\rho$...
3
votes
1answer
54 views

Numbers that are different repeated digits in different bases

Q. What are all the numbers $n$, such that each is represented as repeated digits—different digits—in two different bases $b_1$ and $b_2$. So in base $b_1$, $$ n_{b_1} = c c c \cdots c \...
-1
votes
1answer
26 views

Find Equivalent Classes [closed]

Define the relation $\mathrel{R}$ on the set of non-negative integers $\mathbb{Z} \geq 0$ by $x\mathrel{R}y \iff 11 | 3x+8y$ Can someone please help me figure out what are the equivalence classes $...
2
votes
1answer
66 views

Simplest Unhalvable Shape

Consider a connected 3D-printable shape such as the below. It appears that any plane passing through the centroid will divide the shape into more than two pieces. Define a shape with this property ...
1
vote
1answer
119 views

Problem solving using logic - 3 person card game [closed]

Three logicians played a game with a set of 21 cards each with a different two-digit prime number. Each drew a card and held it up so that they could not see their own card but could see the cards of ...
2
votes
1answer
93 views

How does the three piles magic trick work?

When I was growing up, my parents taught me a simple magic trick that consisted in making three piles of cards and guessing my card, even when they hadn't even touched the deck. The trick in itself ...
4
votes
1answer
68 views

Sum of the square of a recursively defined function

This problem is from a math competition from 1994. I have been having trouble working with this problem: Let $f(1) = 1, $ and $f(n + 1) = 2\sqrt{f(n)^2 + 1}$ for $n \geq 1$. If $N \geq 1$ is an ...
0
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1answer
44 views

Where Have I Gone Wrong? 2 Combinatorics Problems

Three physics books, five biology books, a dictionary and two comic books are stored on a bookshelf. (a) Determine the number of possible arrangements where the two comic books are not next to each ...
1
vote
1answer
38 views

Comparing the number of real numbers between 2 ranges

I know that there are infinitely many number of real numbers between (1,2), (2,3) and so on and I know that there's no meaning to compare the number of real numbers between 2 ranges of real numbers ...
8
votes
1answer
146 views

Symmetric monotonic function $f$ on $[0,1]^2$ with $\int_0^1f(x,y)dy=x$

I am searching for an almost-everywhere continuous and monotonic function $f:[0,1]^2\to[0,1]$ with the following properties: $f(x,y)=f(y,x)$ $f(0,y)=0$ and $f(1,y)=1$ (so $f(0,1)$ and $f(1,0)$ are ...
24
votes
11answers
4k views

BIG LIST: Statements that look obviously false but cannot be disproved

I'm looking for statements that look obviously false but have no disproof (yet). For example The base-10 digits of $\pi$ eventually only include 0s and 1s. To make this question a little objective, ...
2
votes
2answers
45 views

Calculating with minimum values [closed]

I'm wondering if there is a mathematical solution to the following. I have a very simple formula of y=x*0,2. However, if x < 100 it should result in 20, if x > 100, it should result in x*0,2. ...
4
votes
2answers
133 views

Digit numbers $\times 2$ [closed]

Some cute results have every digit doubled. \begin{align} 99225500774400 = {} & \frac{40!}{31!} \\[8pt] 33554433 = {} & 2^{25} +1 \\[8pt] 222277 = {} & -22^{2^2}+77^3 \\[8pt] ...
4
votes
0answers
80 views

What is the probability of exactly one negative solution in a Fibonacci system of equations?

The Fibonacci numbers denoted by $F_i$ for $i\ge1$ are $$1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,\cdots$$ where they satisfy the property $F_{i+2}=F_{i+1}+F_i$. I have listed the first $15$ ...
6
votes
0answers
53 views

Nim-Like Game: Subtracting powers of 2 from 1000. [duplicate]

A professor of one of my courses introduced us to a game to play during down-time, we start with 1000, then we take turns subtracting the powers of 2 (1 to 512), from 1000, we can use the same power ...
0
votes
2answers
52 views

Common sum in magic square

A magic square of size N,N ≥ 2, is an N ×N matrix with integer entries such that the sums of the entries of each row, each column and the two diagonals are all equal. If the entries of the magic ...
0
votes
1answer
67 views

determine every function $f$ defined for positive numbers

determine every function $f$ defined for positive numbers , having positive values, such that : $f(xf(y))f(y)=f(x+y)$ $f(2)=0$ $f(x)\neq 0$ for every $0\le x<2$ Iproved that $f(x)=0$ for every $...
0
votes
3answers
61 views

How do I solve $z+z^{-1}=2\bar z$ using $z=x+iy$ and $\bar z =x-iy$ substitution? [closed]

How do I solve $z+z^{-1}=2\bar z$ using $z=x+iy$ and $\bar z =x-iy$ substitution? zconjugate is also $\bar z$ in some countries.
2
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0answers
105 views

Mathematics: A Spectacular Sport. Are there (unscripted) vlogs of people actually doing mathematics?

Are there vlogs of people regularly attempting to solve mathematics problems, warts & all? I haven't found any. I know of puzzle-attempt YouTube channels, like CanChrisSolve?, so why aren't ...
0
votes
1answer
94 views

How can I use four 7's to equal the number 87? [closed]

How can I use four 7's to equal the number 87? Help is greatly appreciated!
6
votes
3answers
77 views

Why is $x^n\approx \left(n(x^{1/4096}-1)+1\right)^{4096}$?

There's an old-school pocket calculator trick to calculate $x^n$ on a pocket calculator, where both, $x$ and $n$ are real numbers. So, things like $\,0.751^{3.2131}$ can be calculated, which is ...
4
votes
1answer
38 views

Geometric probability - challenging problem(two points of a square K determine a diagonal of another square that is contained in given square K)

Let $K:=[0,1]^{2}$ be a square on $\mathbb{R}^{2}$. We select 2 random points $A$, $B$ $\in [0,1]^{2}$ in this square. What is the probability that the square, whose diagonal is the line segment $AB$, ...
3
votes
1answer
69 views

A curious variant of the classical 2D random walk: allowing duplication and vanishing

Background. Recall the standard random walk on a 2D grid (i.e. $\mathbb{Z}^2$). A person starts at the origin. At every iteration, the person moves in one of the four directions (up, down, left, or ...
1
vote
1answer
43 views

bucket numbers by range

I have a list of numbers: 0,1,2, 200,220,240, 310,330, 371,380,390 I want to put these numbers into four buckets using range with value 40 for example. 0,1,2 are all in range 40. So they ...
1
vote
1answer
44 views

What recommendations can be used to speed up solving a logic puzzle problem involving placing in order a set of elements using a logic grid?

The problem is as follows: A group of archaeologists found an artifact to which they believe tells an account of the results of a race in an ancient Hippodrome. After days of studying the ...
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votes
1answer
32 views

An algorithm to convert a number to a decimal

Does anyone know a simply conversion algorithm to turn a number range of 1 to 10 into a decimal range of .5 to 1? Even more complicated (to me), another algorithm to covert a range of -1 to -10 into ...