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

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3
votes
3answers
55 views

Unbounded sequence with convergent subsequence

I'm just wondering if anyone knows any nice sequences that are unbounded themselves, but have one or more convergent sub-sequences?
0
votes
1answer
48 views

How often does $p^k$ divide the Fibonacci numbers?

I would like to know about the Fibonacci numbers $F_n = 1,1,2,3,5,8, \dots$ in $\mathbb{Z}/p^k\mathbb{Z}$. $$ \mathbb{P}[p^k \text{ divides } F_n ] = \frac{\#\{1 \leq n\leq N: F_n \equiv 0 \mod ...
5
votes
1answer
116 views

Geometrical question just for fun

Was puzzling with the following (home made) puzzle: Given the square $ABCD$ with $A = (1,1)$, $B = (1,-1)$, $C = (-1,-1)$ and $D = (-1,1)$ And given point $E = (0,2)$ What is the smallest (by ...
1
vote
2answers
52 views

Arrangement of Numbers to Get a Common Sum

I'm having trouble with a math problem. I need to arrange 6 numbers on a certain diagram: At every intersection of two circles, I have to put one of these six numbers: 4, 5, 5, 6, 6, or 7. The sum ...
6
votes
6answers
348 views

Do the differences of perfect squares apply to perfect cubes and more?

I'm curious about a special property of squares. The difference between perfect squares starting from 0 are 1,3,5,7,9..., where each difference goes up by 2. I want to know if there are any patterns ...
3
votes
2answers
51 views

Mandelbrot Set Equation

Is there a graphable equation that graphs the Mandelbrot Set? It seems like an interesting design, but I want to find a way to show all of the details via a graphing calculator.
1
vote
2answers
156 views

Puzzle with pirates

That one I'm pretty low on ideas of how to approach it. Five pirates of different ages have a treasure of 50 gold coins. On their ship, they decide to split the coins using this scheme: The oldest ...
3
votes
1answer
87 views

Marriage puzzle

I need some insight for the following problem: There are 100 girls and 100 guys. The girls each have their individual preference list for which guy they’d like to marry. Each list contains all 100 ...
1
vote
2answers
61 views

Continue the sequence

I'm stack at that question as I'm not sure which law does the sequence obey What number comes next in this series: 1 11 21 1211 111221 312211 13112221: 12113331 1113213211 13221113 ...
3
votes
1answer
70 views

Paint a cube with 6 colors

I have a unit cube and $6$ colors to paint its sides in. How many different cubes to I get if I use one color per side? I think I know the answer, but just want to be sure regarding my solution. Let ...
5
votes
4answers
674 views

How to solve a puzzle with numerals

Any insights are welcome for this puzzle. The following equation is wrong: $103 - 102 = 3$. Move one numeral to make it correct. The numeral moved is: $0,1,2$ or $3$?
1
vote
1answer
94 views

Question About the Solutions to the Eight Queens Problem [closed]

How is $a_{15}n_8e_9k_5f_{10}d_7b_4m_6$ a solution to the Eight Queens problem? J. W. L. Glaisher, On the Problem of the Eight Queens, Philosophical Magazine, 1847 says that each one of these terms ...
-3
votes
1answer
56 views

How to solve the expression $x^b-y^b=z^b$? [closed]

I would like to simplify $x^b-y^b=z^b$, but I want to be able to write $z$ in terms of $x$ and $y$, and not $b$.
4
votes
0answers
37 views

Derangements and the “other” secretary problem

I just found out that the name "Secretary problem" is given to two different problems. The first one talks about a secretary who mixes letters and envelopes, and ask for the probability that no letter ...
0
votes
3answers
314 views

Probability that a leap year has 52 Sundays

For the Question "Find the probability that a leap year has 53 Sundays". The Solution goes : For 53 Sundays, we proceed as: $\frac{366}{7} = 52.28$; So we can be sure that there are 52 Sundays, ...
1
vote
3answers
76 views

Find Differences between Ages of A and B.

Question: A says to B, I am twice as old as you were, when I was as old as you are. If the sum of ages is 63 years. Find the difference between their ages. My Question: I understand that we need to ...
0
votes
1answer
70 views

Liar - Truth-Sayer - Tourist Problem. Construct the answer with the given 2 sub-statements.

A tourist A comes to a country where people are divided into two categories: Liars (L) and Truth Sayers (T). Ls always lie and Ts always speak the truth. Intending to walk to the capital, the tourist ...
3
votes
2answers
80 views

2 Trains and Fly Problem. Find the number of trips made by the fly back and forth.

Question: A Train A is approaching at a speed of 10m/sec, another Train B moving in the opposite direction at a speed of 20m/sec. A fly whose absolute speed is 50m/sec goes repeatedly from A to B and ...
0
votes
1answer
92 views

What is the subset of the letters in the word 'numbers'

What is the subset of the letters in 'numbers'? I thought it meant to make a word out of the letters in 'numbers' so I tried to make a word out of it, but I couldn't make a word and so I don't ...
0
votes
1answer
89 views

The famous Portia's casket problem

Gold casket: the portrait isn't in the silver casket. Silver: the portrait isn't in this casket. Lead: the portrait is in this casket. At least one of the statements was true and at least one of them ...
8
votes
2answers
359 views

Euler's identity in matrix form

I assume everyone is familiar with the famous mathematical identity due to L. Euler: $$ e^{i \, \pi} + 1 = 0,$$ where $i^2 = -1$ and $e$ is the base of natural logarithms. I was wondering if this ...
0
votes
1answer
90 views

Solve Spherical Shell for Radius given Thickness and Volume

I'm looking to calculate the outer radius of a spherical shell of a desired volume and thickness. I don't know if the years have knocked some obvious obstacle out of my perception, but here's what ...
1
vote
1answer
29 views

Find a polynomial mod $n$ injective on a given set

This question is inspired by this challenge on CodeGolf.SE, in which the goal is to create a hash function with specified collisions. I thought a polynomial over the integers mod $n$ might be a nice ...
0
votes
1answer
62 views

Repeating cycles in the $3n-1$ problem

While tracking sequences beginning with 1-to-3 digit integers, I have found 3 different repeating cycles in the $3n-1$ problem (similar to the Collatz Conjecture). They are 1, 2, 1..., 5, 14, 7, 20, ...
1
vote
0answers
40 views

Tools (electronic notebook and ontology viewer) of mathematical formulas (definitions and facts)

I am reading math books and articles (for applications in other disciplines, mostly about logics for computer science and AI) and the hardest part is to memorize formulas, to look up some ...
19
votes
12answers
727 views

hand evaluate $\sqrt{e}$

I have seen this question many times as a example of provoking creativity. I wonder how many ways are there to evaluate $\sqrt{e}$ as accurately as possible. The obvious way I can think of is to use ...
1
vote
1answer
56 views

Finding the minimum value of a 6th degree polynomial algebraically

Is it possible to answer this question using methods of basic algebra? Find the least value of the expression $a^6 + a^4 - a^3 - a + 1$ for real value of $a$. This question is from the 2013 Philippine ...
1
vote
2answers
274 views

Is it possible to reach 50k in the game 2048 with only having a highest tile of 512?

Is it possible to reach a score of 50,000 in the game 2048 with only having a highest tile of 512(Only one 512 was present) and one 256 tile and other small numbered tiles such as 2,4,8,16,...,64. ...
2
votes
1answer
88 views

Getting multiple of 11

Take any $2$ digit number having different digits. Now add the bigger digit in that number. By continuing this process, you will get a multiple of $11$ i.e. both of the digits will be equal of a ...
4
votes
4answers
483 views

What does “twice as likely” mean?

Once in a while I hear people say something like X is twice as likely as Y. What they usually mean is: $$p(X) = 2 \cdot p(Y)$$ and - in the context they refer to - they usually have $p(Y) < ...
7
votes
2answers
137 views

What is the integral $\int x^t/\Gamma(1+t) \, dt$? (In general: relation between series and integrals)

(The question arises from playing with translating series into integrals) I wanted to see, what it means to have a "continuous" relative for powerseries and other series; the most simple one ...
0
votes
2answers
319 views

Google Code Jam's Cookie Clicker Program…

Today, the Google Code Jam's cookie clicker problem was something like this. Problem In this problem, you start with 0 cookies. You gain cookies at a rate of 2 cookies per second, by ...
1
vote
1answer
127 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
2
votes
2answers
76 views

Orthogonal tangents to an ellipse [duplicate]

This is the problem I found back in the first year in the university. Suppose we have a non-degenerate (i.e. not a point and not an empty set) ellipse $E\subset \Bbb R^2$. Now define a set $D$ by a ...
3
votes
2answers
288 views

Horse Race Math question

There are 25 horses. You can take 5 of the horses at a time and race them. Each horse always finishes the race in the same amount of time, and there are no ties. The only information you get from each ...
0
votes
0answers
35 views

Horse Race Math: Determine the top fastest 3 of 25 horses in the fewest number of races possible. Help! :) [duplicate]

There are 25 horses. You can take 5 of the horses at a time and race them. Each horse always finishes the race in the same amount of time, and there are no ties. The only information you get from each ...
1
vote
2answers
86 views

“Relatively Close” Soccer Game

A soccer game between 2 teams is "relatively close" if the scores never differ by more than 2. In how many ways can the game be "relatively close" for the first 12 goals? Just to clear it up, the ...
99
votes
10answers
13k views

How can a piece of A4 paper be folded in exactly three equal parts?

This is something that always annoys me when putting an A4 letter in a oblong envelope: one has to estimate where to put the creases when folding the letter. I normally start from the bottom and on ...
0
votes
1answer
53 views

Which performance enhancement is better?

Suppose you are given the task of improving the performance of a program consisting of three parts. Part $A$ requires 20% of the overall run time, part $B$ requires 30%, and part $C$ requires 50%. ...
5
votes
0answers
142 views

Coding Theory Problem to save Humanity

For starters, this problem doesn't originate from me, it's a friend's coding theory problem and I got interested, thinking about it, but I can't think of any as I only have very basic coding theory ...
1
vote
1answer
63 views

Recreational Mathematics title search

I once read part of a book on recreational mathematics that told a variety of stories. A central part of each story was a piece of non-trivial, and very interesting mathematics: the sofa moving ...
4
votes
1answer
76 views

A game problem- double or increment by 1

Its a two player game. Initially $P=1$, and there is some fixed integer $Q>1$. A valid move consists of either increasing $P$ by $1$ or doubling it iff on doing so $P$ does NOT exceed $Q$.The ...
8
votes
2answers
118 views

“The Mario Party Problem”

My roommate and I were trying to figure this one out last night after a heated game of Mario Party: This is a minigame in Mario Party that pits 3 players on a team against 1 solo player. The game ...
25
votes
3answers
2k views

Constructing a Möbius strip using a square paper? Is it possible?

I understand that, from a topological perspective, it is irrelevant whether we choose the quotient of the square $[0,1]\times [0,1]$ (by identifying points $(0,t)$ and $(1,1-t)$) or the quotient of ...
2
votes
0answers
104 views

Given a number of items, how many sets of three are there where no two sets are two thirds similar?

Sorry if the title isn't proper math-talk. Hopefully I can explain it better here. So let's say we have a set. 1, 2, 3, 4, 5, 6, 7, 8, 9. I want to know how many groups of three can be made where no ...
1
vote
1answer
78 views

Simple Circle Problem

An elegant circle problem. It goes by many names. This is my version. Dog 1 is tied to a post by a leash 1 unit long. He shares half of his land with Dog 2 tied to a post 1 unit away from his own. ...
4
votes
5answers
246 views

Find the results of the race using the given 5 conditions.

There are five competitor A, B, C, D, and E and they enter a running race that awards gold, silver, and bronze medals. Each of the following compound statements about the race is false, although one ...
0
votes
4answers
1k views

Find the least value of x which when divided by 3 leaves remainder 1, …

A number when divided by 3 gives a remainder of 1; when divided by 4, gives a remainder of 2; when divided by 5, gives a remainder of 3; and when divided by 6, gives a remainder of 4. Find the ...
4
votes
1answer
111 views

How to win this game?

I have a challenge: to win the game with the following rules: There are exactly two players and their turns alternate; At each turn, a player removes 1, 2, 3 or 4 counters from a pile that was ...
0
votes
1answer
104 views

Find the width of the river.

Q) 2 boats are crossing the river from opposite sides. When they first meet, they are 720m from the near shore. When they reach the opposite shore, they stop for 10mins and cross the river again, but ...