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Questions tagged [recreational-mathematics]

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

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Find the nearest balanced integer

OEIS A036301 is a sequence of numbers $ n $ such that the sum of the even digits of $ n $ equals the sum of the odd digits of $ n $. Let's call these numbers "balanced". Given an input positive ...
9
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2answers
134 views

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

I came across a puzzle in a Maths Calendar I own. Most of them I can do fairly easily, but this one has me stumped, and I was hoping for a hint or solution. The question is: What are the solutions to ...
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0answers
28 views

Roulette Expected Winnings Discrete Math

Someone is playing Roulette. Here is an example of an outcome: If a player bets on a single outcome the payout is 35 to 1 – meaning if the player guesses the correct answer and puts down a dollar, he/...
1
vote
1answer
21 views

Solutions to a polynomial equation with constraint

I am looking for solutions to the following simple polynomial equation, $$ x_1^2 + x_2^2 + y_1^2 + y_2^2 = -2 (x_1 x_2 + 3 y_1 y_2) $$ where $x_i, y_i \in \mathbb{R}$. Importantly, I would like only ...
0
votes
1answer
13 views

Determining the values for an array within limits

So I did some math on a function to produce positions within an array of which I wanted to record data. My initial math looked like this: $$ (n * \frac{100}{n})-1$$ This would allow me to determine ...
0
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0answers
24 views

Maximum number of rounds needed for a multiple strike tournament

I have a spreadsheet set up that will allow me to track video game tournaments (although it can be used for other types of tournaments as well). The formulas that I created the spreadsheet with ...
0
votes
1answer
38 views

Maximum number of kings on the chessboard subject to some rules

The chess king moves one square in any direction (horizontally, vertically, or diagonally). The goal is to place as many king as possible on an r×c board subject to the following two conditions: ...
1
vote
1answer
57 views

Largest smallest value in sudoku like puzzle

In this post, a sudoku like math puzzle is proposed. The grid must be filled while respecting a unique constraint : the sum of all $3\times3$ sub-squares must equal $2019$. It is not that difficult ...
3
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1answer
65 views

A puzzle about the maximum number of favorable squares on a board of any given size.

I have come up with an interesting puzzle but I can't for the life of me figure out how to solve it. It follows like this: You have 2 types of squires that are congruent with one another. Let's call ...
6
votes
2answers
114 views

How many solutions are there for the equation $a^x = \log_a x$, where $0 < a < 1$?

How many solutions are there for the equation $a^x = \log_a x$, where $0 < a < 1$? When I first saw this quiz for japanese high school students, I wondered there was only 1 solution for the ...
5
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0answers
58 views

Two players placing coins on a table- Extension

The origin of my question comes from a common job interview question where two players take turns placing coins on a round table. The coins cannot overlap and can't be moved once they've been placed. ...
2
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1answer
67 views

Radioactive coins - find the two radioactive coins out of twelve

Here is a beautiful problem: Given twelve coins, exactly two of them is radioactive. There is a machine. You are able to put some of the coins into the machine, and then the machine tells if the ...
7
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0answers
69 views

Determining finitude or infinitude from a simple geometric construction

Playing with a pencil on a checkered sheet I encountered this construction: 1) take a point $A$ on the grid and a point $B$ that is distant from $A$ $n=2,3,4...$ horizontal steps and $1$ vertical ...
1
vote
1answer
53 views

Cover the plane with closed disks

Help with this Putname problem: Is it possible to find an infinite sequence of closed disks $D_1,D_2,...$ in the plane with centers $c_1,c_2,...$ such that a) the $c_1$ have no limit point in the ...
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0answers
27 views

Books like “Jeux de l'esprit et divertissements mathématiques”

I have enjoyed the second edition of the title's book (Nouveaux jeux de l'esprit et divertissements mathématiques) and now I have bought the first edition. To set some context, the book has some "...
9
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2answers
117 views

Is it always possible to fit these pieces in a square?

Consider all possible pairs of squares that can fit in a row of length $n$ where every square has a width of 1. If I have a large square of width $n$, can all such pairs of squares fit in the large ...
0
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1answer
55 views

Using (rigid) Origami moves only, what is the maximum volume that can be enclosed by a square piece of paper?

Motivation: This is inspired by this question. The Question: What is the maximum volume that can be enclosed by folding a square piece of paper (with side length $\ell$) using only (rigid) ...
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2answers
68 views

Probability of two dice against one

If you roll two dice, what are the odds that at least one has a higher value than a third die you roll?" And for (B), it's the same as (A) except you roll three dice before checking against a fourth?
1
vote
1answer
45 views

Probably of winning with 2 dice (maximum of them) against another one

could some of you help me to find out what is the probability of A) obtain with two dice a greather number than another die? B) and if the dice are 3 how can I do? Not the sum of the 2 dice, but the ...
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votes
1answer
35 views

Probably of winning with 2 dice against 1

could some of you help me to find out what is the probability of A) obtain with two dice a greather number than another die? B) and if the dice are 3 how can I do? Not the sum of the 2 dice, but the ...
2
votes
2answers
49 views

Trig and Triangle Math Club Question: Finding Side Length

I recently had a math club competition, and I was unsure of how to approach one of the problems on the test: In $\triangle ABC$, $\ \ \ \ \ \ \ \ \cos(2A-B) + \sin(A + B) = 2$ $\ \ \ \ \ \ \ \ \...
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2answers
43 views

How can we cut a 3D Cube using 3D Cube?

Cutting a 1D Line: We can cut a 1D line via 0D point. if we want to cut a 1D line via a 1D line. we have to move 1 dimension up that is in 2D (Image for 1D Line ...
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0answers
299 views

The Complexity of “The Baby Shark Song”.

This question is just for fun. I hope it's received in the same goofy spirit in which I wrote it. I just had the pleasure of reading Knuth's "The Complexity of Songs" and I thought it'd be hilarious ...
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0answers
22 views

Why only add the odd rows and not the even rows in Russian Peasant [duplicate]

I've read through a load of information and proofs regarding the Russian peasant multiplication method but none of them are explicit when describing the addition stage. Why is it only the odd rows we ...
0
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1answer
61 views

Show that the first child can not win

Three children have 10 pieces numbered from 0 to 9 on both sides. They play the following game: -The first child chooses a piece, so a number, preserves it and passes the number on a sheet -The ...
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votes
2answers
51 views

Logical Induction

"Prove that the number of people making an odd number of handshakes is always even." Though it can be easily proved by Induction but I wanted to ask is it correct to state the problem otherwise like "...
2
votes
2answers
31 views

A directed complete graph with equal number of incoming and outgoing edges [duplicate]

In a complete graph with $n$ vertices, every vertex has $n-1$ edges. Assuming $n$ is odd, the number of edges from each vertex is even. If we now give every edge an orientation (making the graph a ...
2
votes
1answer
59 views

Pascal-like Triangle Relation

I was fiddling around with an expansion, trying to find the coefficients of a certain formula, and I found that they satisfied the following relation for $0 \leq c \leq r$ $$ N(r,c) = \left\{ \begin{...
0
votes
1answer
491 views

Circles with diameters $3$, $4$, $6$ are packed in a rectangle of width $6$. Find a particular length.

I'm trying to solve a simple problem that someone sent me. From $A$ to $A^\prime$, I calculated the length to be $\sqrt{6}\text{ cm}$; and from $A^\prime$ to $B$, I got $\sqrt{24}\text{ cm}$. I'm ...
9
votes
1answer
138 views

The Mathematics of Coca Cola's Ribbon Wrapper.

I'm sorry if this is too vague a question or is otherwise deemed poor quality. The Background: I've just seen an advert for the (new?) Coca Cola festive ribbon wrapper. Here's a picture: A ...
8
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0answers
104 views

How can we formalize Jorge Luis Borges' Aleph?

Background. Jorge Luis Borges was a post-modern short-story writer of the 20th century, whose stories often invoke a healthy dose of surrealism. One of his works is called The Aleph. In this book, ...
6
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0answers
73 views

What's up with the cycloid-shaped pot in Melville's Moby Dick?

People interested in the intersection between mathematics and fine literature may be familiar with the following quote from Herman Melville's famous novel Moby Dick: It is a place also for profound ...
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0answers
69 views

Is this fractal equation complete?

Background I recently asked this question: Can this strange implicit matrix equation be solved?. Followed by Is this "fractal equation" for fractals constructed by finite subdivision rules ...
2
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0answers
54 views

How to adjust the curve of a sine wave formula? [closed]

Apologies to all I'm pretty ignorant to maths beyond high school level. Essentially what I want to do is create a sine wave that's a bit more curvy than just a standard sine wave (see image below) I'...
8
votes
1answer
45 views

How can I describe the vertical component of a juggling ball's path with a sine wave?

I juggle, and then track the juggling balls. I want to describe this juggling trick using sine waves. A metronome was used to keep the throws periodic. The video is 120fps, so there are 120 ...
1
vote
1answer
88 views

What is the minimum amount of moves it takes to finish this game?

This is a follow up question from this post which I asked. The previous question was answered by Barry Cipra, and I was suggested to create this follow up question. The Game: Two players have $...
0
votes
1answer
48 views

Parasitic number, where does their name come from?

Parasitic numbers, they are nice for recreational purposes, where I got notice of them (I found some of them by considering the solvability of a suitable diophantine equation). But, I couldn't figure, ...
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0answers
35 views

Arranging coins [duplicate]

A student enjoys collecting antique loonie coins and counting problems. Their collection has gotten quite large and they are trying to arrange them nicely into groups. If the coins are ...
7
votes
1answer
1k views

Rolling icosahedron Hamiltonian path

A cube has 24 orientations. By rolling the cube on its edge within the perimeter of a $2\times4$ rectangle 3 times, all 24 orientations are reached and the next roll returns the cube to both the ...
0
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2answers
49 views

How to calculate the total width of an object with a radius

I am trying to figure out how I can calculate the total width of an object with a radius. The following dimensional images I have only show the width of the object itself, not the total width. I ...
0
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1answer
29 views

What type of mathematics is this problem? (Scheduling maybe? I don't know what to search for to find help.)

Sample Problem: A well can supply 50 laborers per day. 40 laborers can build a new well in five days, up to 10 total. Each laborer can complete 1 stone per day. The new temple needs 5000 stones. *** ...
4
votes
3answers
77 views

Basic maths: Interview question getting proportion from averages

It's probably simple but I was given this question in a video interview recently and I spent ages coming up with two different answers. (please let me know if this is the wrong place for this, I'm ...
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0answers
23 views

How can I create currency note count calculator if I have currencies which has decimals and total amount which also has decimals?

If i have currencies that are in decimals {0.7,0.8,1.4,0.5} and total amount which also has decimals (example: 1279.6) and I tell you that you need to make total within certain number of currency note ...
1
vote
1answer
69 views

Math sticker meanings [closed]

I am trying to understand what these stickers mean. The ones on the top row are: Good one! I am impressed! (I know $\sum x_n /n$ is the mean of the $x_i$, but I don't understand this one) The ...
1
vote
1answer
50 views

Lexicographically smallest sequence of integers not in the OEIS

A sequence $a_i$ ($i=1,\ldots$) is lexicographically smaller than sequence $b_i$ if either $a_1 < b_1$, or $a_j = b_j$ for $j=1,\ldots, k$ and $a_{k+1} < b_{k+1}$. If I asked for the ...
3
votes
1answer
45 views

Probability of winning a 7-game series if you win game no. $j$

This question is inspired by the ongoing baseball playoffs, but pertains to any tournament where 2 teams play a 7-game series, where the first to win 4 games is the overall (series) winner. In times ...
2
votes
0answers
71 views

A Logic Puzzle: Explanation Of The Solution

I am trying to understand the solution to a logic puzzle, but it confuses me on many levels The problem is this: And the solution is this: What confuses me is the following: Why would it ...
0
votes
1answer
110 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 ...
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votes
1answer
52 views

How to guarantee entry into cave [closed]

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 ...
2
votes
0answers
50 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 ...