Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [recreational-mathematics]

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

0
votes
0answers
24 views

Calculating amount left at the end of a repetitive cutting down cycle

Let's say I have a group of X's characters that I want to cut down. I use a method similar to 'find-and-replace-all' tool, which takes an amount of X's each time, deletes them, and replaces them with ...
2
votes
2answers
79 views

How many tuples of {$a, b, c, …$} satisfy $abc… \leq n$?

Let $n$ and $k$ be positive integers. Let $a, b, c, ...$ be $k$ positive integers such that $abc... \leq n$. How many tuples of {$a, b, c, ...$} satisfy the inequality? Note that the tuples {$a=1, ...
2
votes
1answer
35 views

Algorithm generating subset of primes, can we classify which of them or estimate how large percent of primes are generated?

Assume I have following algorithm: Two lists of numbers, first starting at 2, second starting empty. We now follow rule: Add a number to first list which makes difference with latest number the ...
1
vote
2answers
64 views

Even stronger than Sophomore's dream [duplicate]

Sophomore's dream states that: $$ \int_0^1x^{-x}dx=\sum_{n=1}^\infty n^{-n} $$ and $$ \int_0^1x^{x}dx=-\sum_{n=1}^\infty(-n)^{-n} $$ A friend of mine noticed that numerically: $$ \int_0^1\int_0^1(xy)^{...
26
votes
0answers
620 views

Mathematics for the afterlife

Paul Erdős said this about the $3n + 1$ conjecture: Mathematics may not be ready for such problems. Similarly, there are parts of mathematics that I am not yet ready for. Some things, however, I ...
0
votes
0answers
31 views

“implied multiplication” operator precedence?

I hold a masters in computer science from one of the worlds top universities and until today I thought I more or less know basic math. I'm sure you guys all know these click-bait simple "90% of ...
0
votes
1answer
45 views

Alternation of Rationals and Irrationals?

I'm in a lunch group at work of recreational math geeks and we came up with a question which we need help to resolve. I apologize in advance, if my explanation is not perfectly rigorous. Given these ...
0
votes
0answers
35 views

Mathematical card tricks

For quite some time I have taken interest in analyzing card tricks that make use of a deep knowledge of advanced mathematics and there's been some progress. However, all the tricks I've tried decoding ...
-2
votes
1answer
40 views

How many solvable and unsolvable problems exist

I am unable to quantify it as there are many problems which are in polynomial time and certain problems can be reduced to polynomial time.How exactly to quantify them?
0
votes
0answers
26 views

Calculating the parity of number of heads on a 8x8 chessboard?

Below is an article where I facing a problem! Please refer this completely before answering my question! Impossible Escape : http://datagenetics.com/blog/december12014/index.html I got all the sub-...
0
votes
1answer
87 views

Discretizing a mathematical equation

This is a 3D map that maps every $(x,y,z)\to (x',y',z')$ uniquely. If i want to implement it's discrete counterpart on matlab platform, i do the following $$\text{if} (i<=\dfrac{n}{2} \wedge ...
0
votes
0answers
32 views

A D20 (dice) has sides where $N-1,N,N+1$ are always neighbours on surface of solid. For which DN is this possible?

A regular gon D20 dice used for example in various forms of gambling and trading card games is shown below As can be seen each number $N$ residing on some face has two of it's neighbouring faces with ...
0
votes
0answers
35 views

Puzzles and exercises to improve mathematical intelligence and spatial thinking

In your childhood or adolescence, or maybe as an adult, have there been types of exercises or puzzles that you think have improved your mathematical intelligence and in particular the spatial thinking?...
10
votes
3answers
657 views

How to minimise the cost of guessing a number in a high/low guess game?

In a high/low guess game, the "true" number is one of $\{1,\cdots,1000\}$. You'll be told if your guess is $<,>$ or $=$ the true number for each guess you make, and the game terminates when you ...
24
votes
1answer
913 views

Strange acknowledgment in Serge Lang's Linear Algebra

Recently I open this book to look up a certain theorem and saw something peculiar about the acknowledgments I've never notice before: Acknowledgments I thank Ron Infante and Peter Pappas for ...
1
vote
2answers
33 views

Solving a statement question based on reasoning and logic.

The question is as follows, In the Land of Liars there are exactly three Clans. Black clansmen always tell lies. White clansmen always speak the truth. Red clansmen are sometimes truthful. A,B and C ...
2
votes
1answer
22 views

Constructing an “Announcement Bingo” card with highest chance of win

There's an event coming up where $FAVORITE_COMPANY is going to announce a bunch of upcoming products. A fan of that company has 25 anticipated/desired announcements, ranked by likelihood, and wants to ...
-1
votes
1answer
80 views

What's a minimal origami construction realizing a cube root?

The constructible numbers are those that can be achieved as lengths of line segments via compass and straightedge, starting with a segment of length $1$. The origami (constructible) numbers are those ...
0
votes
1answer
49 views

Hard puzzle about people walking in the street. [duplicate]

We have a 1 dimensional street (straight) where people can either walk left or right. They all walk with the same speed. If two people meet they instantly change their direction (without loss of speed)...
3
votes
6answers
89 views

Equation of the line that lies tangent to both circles

Consider the two circles determined by $(x-1)^2 + y^2 = 1$ and $(x-2.5)^2 + y^2 = (1/2)^2$. Find the (explicit) equation of the line that lies tangent to both circles. I have never seen a clean or ...
2
votes
4answers
160 views

Why $(-2)^{2.5}$ isn't equal to $((-2)^{25})^{1/10}$?

I've tried both calculations on Wolfram Alpha and it returns different results, but I can't get a grasp of why it is like that. From my point of view, both calculations should be the same, as $2.5=25/...
0
votes
0answers
20 views

General formula for the $(i,j)$ term in number spiral? [duplicate]

Several times I have to do with this configuration: \begin{pmatrix} & & & & & & & & & & \\ & & & & & & & & &...
1
vote
1answer
65 views

best cut for microwave oven

Suppose, that there is a Pizza which is round and has radius $1$. Now one would like to find the best way, under $n$ cuts, to cut the Pizza so as to obtain the minimum 'Microwave Oven Distance'- For ...
1
vote
2answers
99 views

How to find the total number of auras possible for a tile of a given tier?

PLEASE NOTE! A different problem that uses the same ruleset (technically a subset of this one since i ask multiple questions here) that can be solved with brute force and pen-and-paper has been posted ...
5
votes
1answer
148 views

Is there a palindrome prime $p>3$ that is also palindrome in base $\ 5\ $?

A prime $\ p\ $ is called palindrome, if the digits in reverse order give the same prime. For bases $\ b=2,3,4\ $ , there are large examples of palindrome primes that are also palindrome in base $b$ , ...
1
vote
2answers
107 views

The Connect Infinity game

Recently Joel David Hamkins posted an entry on the Connect Infinity game. Connect-$\omega$ is Connect Four but played on an $\omega\times n$ grid ($n$ finite)! The above shows $n=6$. The difference ...
-3
votes
1answer
52 views

Equation of Tango dancing [closed]

Good evening! I have been encouraged to ask my question on this forum, even though it might be perceived as a pure subjective and open-ended question, but I am 100% sure there is a perfectly ...
0
votes
0answers
23 views

Calculate most efficient combination of group payment transactions

Me and my roommates don't split expenses right away but enter the amounts paid for others into a spreadsheet. So at the end of the month, we can pay each other the residual amounts. We discovered that ...
1
vote
1answer
38 views

how to re-organize the classes

There are $m$ Reception (R) classes in a school, each contains $n$ students, $m|n$. In September all $mn$ students will be in Primary 1 (P1). In P1 there will still be $m$ classes each with $n$ ...
0
votes
0answers
13 views

Find out non-overlapping schedule to execute jobs

I have a set of 6 jobs to be run via a scheduler. Let's call them jobs A,B,C,D,E & F. 'A' & 'B' take 2 mins to complete, 'C' , 'D' , 'E' & 'F' take 3 min each to complete. No job is ...
0
votes
1answer
55 views

There are 314 coins in 21 open boxes. In each move you can take 1 coin from each of any two boxes and put them into a third box and…

There are 314 coins in 21 open boxes. In each move you can take 1 coin from each of any two boxes and put them into a third box and in the final move you take all the coins from one box. What is the ...
0
votes
1answer
53 views

Minimum number of 'moves' required to re-order a list of numbers

Consider the following 'game'. You have a list of $N$ integers ordered in descending order from $N$ to $1$. The aim of the game is to sort the list back into ascending order. Rules: You can only ...
0
votes
1answer
27 views

Modified Magic square with sum $15$

Consider the following diagram: The task is to use integers from 1 to 9 (both endpoints inclusive) in a way that the sum of all numbers written in 3 square in the same row or column is 15. I think ...
1
vote
1answer
70 views

Second derivative of itself

I know the $ \frac{d^2x}{dx^2}= 0 $, since $dx/dx = 1 ...$ But by playing with some equations it is easy to get that $d^2f/dx^2=f''(x)$, so $d^2f=f''(x)dx^2$ and $df=f'(x)dx$, so $df^2=f'(x)^2dx^2$. ...
2
votes
1answer
56 views

Number of permutations differing in at least $d$ spots in pairwise comparisons

A friend and I were thinking about this problem today but we were unable to come up with a solution. Problem: Consider the the numbers $S=\{1,\ldots,n\}$. Given $2\le d \le n$ what is the ...
1
vote
3answers
83 views

Find the smallest $n$ such that the $n$-th prime $p_n \equiv 330 \mod n $.

Find the smallest $n > 1$ such that the $n$-th prime $p_n \equiv 330 \mod n $. I was investigating the remainders when the $n$-th prime is divided by $n$. For every positive integer $a < 330$, ...
-3
votes
1answer
91 views

How many people are there when the word “with” is used? [closed]

How many people are there is the following statement: "Bob with his family of 4..." Is it: a total of 4 (Bob + 3 members) or a total of 5 (Bob + 4 members) ?
2
votes
3answers
88 views

When to apply negative sign when number is squared

I always had this confusion of when I need to apply the negative sign in the calculation. I understand that $(-1)^2 = 1$ however why isn't $-1^2 = 1$?
2
votes
1answer
51 views

Version of Fitch Cheney's card trick

Fitch Cheney's card trick is well known. Alice picks five cards from a deck. Bob takes them, gives one back to Alice and arranges the other four in some order. Chuck then enters the room, looks at ...
0
votes
1answer
108 views

Why do we not use letters as numbers? [closed]

To me, it seems like such a waste of energy to teach children a new set of symbols $(0,1,2.....)$ after they have learnt the alphabet. Why do we not replace $a=0$ and $b=2$ until $j=9$ and use the ...
0
votes
0answers
26 views

Is there a way to narrow down the choices to the picture below given the price?

So I saw this post somewhere and I’m curious if there’s a way to narrow down the possible things a person did given the total price he/she add up among the things listed in the picture below. https://...
2
votes
0answers
53 views

An order-6 configuration

Here's an example of an order $96_6$ configuration found by L.W. Berman. Every point has six lines, every line has six points. The unique 6,6 cage graph is bipartite and is a Levi graph for the ...
6
votes
1answer
66 views

Long anti-arithmetic permutation

A permutation is a sequence $(a_1, \ldots, a_n)$ in which each number $1, \ldots, n$ appears precisely once. We call a sequence anti-arithmetic if there are no non-trivial arithmetic subsequences in ...
1
vote
1answer
56 views

Generating all possible Domino tilings on a $4 \times 4$ grid

I have a task to write a program which generates all possible combinations of tiling domino on a $4 \times 4$ grid. I have found many articles about tilings, but it is for me quite difficult and I ...
23
votes
1answer
1k views

How to colour the US map with Yellow, Green, Red and Blue to minimize the number of states with the color of Green

I want to colour the US (only the states) map with Yellow, Green, Red and Blue. I was wondering what would be the lowest number of states with the colour of Green. We can of course use the other ...
9
votes
1answer
331 views

Hopping to infinity along a string of digits

Let $s$ be an infinite string of decimal digits, for example: \begin{array}{cccccccccc} s = 3 & 1 & 4 & 1 & 5 & 9 & 2 & 6 & 5 & 3 & \cdots \end{array} Consider ...
0
votes
2answers
94 views

$\frac{\left(10^4\right)}{x^2}=\frac{\left(x^{\left(8-2\log x\right)}\right)}{10^4}$ Solve for x.

$\frac{\left(10^4\right)}{x^2}=\frac{\left(x^{\left(8-2\log x\right)}\right)}{10^4}$ Solve for x. $\frac{\left(10^4\right)}{x^2}=\frac{\left(x^{\left(8-2\log x\right)}\right)}{10^4}\Rightarrow 10^8=\...
1
vote
1answer
55 views

Green-eye paradox (an information paradox) or the Dragon puzzle

I was trying to solve this puzzle but I believe I have run into a paradox.Found the puzzle in https://io9.gizmodo.com/can-you-solve-the-hardest-logic-puzzle-in-the-world-1642492269 "There are 100 ...
0
votes
0answers
11 views

galactic to ecliptic coordiantes

I want to describe the position of a point with an ecliptic coordinate system. Using this celestial coordinate system to represent the apparent position of 3D points is my goal. The output values ...
1
vote
0answers
31 views

Linear equations problem from CAT

How do I solve this question. Here is what I've been thinking: lotion A can relieve 75 spasms and lotion B 120 spasms. So going by options buying only lotion B would be cheaper right? Is my reasoning ...