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

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2
votes
1answer
435 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
259 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 ...
7
votes
3answers
1k views

Horse Race question: how to find the 3 fastest horses?

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
60 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
166 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 ...
151
votes
12answers
24k 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 ...
1
vote
1answer
190 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
1answer
210 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 ...
3
votes
1answer
112 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 ...
6
votes
1answer
322 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
266 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 ...
28
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
723 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
99 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
353 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 ...
1
vote
4answers
5k 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
153 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
173 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 ...
5
votes
2answers
337 views

A strange lier that tells truth on 7th day of the week.

Q)Ravi is strange liar. He lies on 6 days of the week, but on the seventh day he always tells the truth. He made the following statements on 3 successive days: Day1: "I lie on Mon and Tue." Day2: "...
3
votes
0answers
101 views

Josephus Variant

I set myself the challenge of trying to solve a variant of trying to solve a variant of the josephus problem where instead of killing every second person, every third person dies. The formula for the ...
51
votes
11answers
28k views

Can a piece of A4 paper be folded so that it's thick enough to reach the moon?

While procrastinating around the web I stumbled on a page that contained the image below, from cracked.com. I can't help but believe that this is false… Even though the article header says: ...
9
votes
2answers
303 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
3
votes
2answers
287 views

Is there a solution to this Seating Plan problem?

So a colleague asked me for some Help on an interesting Problem, which we both couldn't find the optimal answer for. The event which needed it is already in the past, so this is just me trying to ...
0
votes
1answer
73 views

Calculate Income Of the Month [Puzzle]

Mr. Jill requires Rs 6000 per month to maintain his family. He saves 20% of any amount that he earns above Rs. 6000 but below Rs 7000 in a month. He saves 30% of amount that he earns above Rs 7000 but ...
7
votes
0answers
196 views

Knight's metric: ellipse and parabola.

Knight's metric is a metric on $\mathbb{Z}^2$ as the minimum number of moves a chess knight would take to travel from $x$ to $y\in\mathbb{Z}^2$. What does a parabola (or an ellipse) became with this ...
34
votes
3answers
4k views

Can a Rubik's cube be mapped knowing only two sides?

Is it possible to know the entire configuration of a Rubik's cube looking at only two sides and not rotating the cube? In other words: what is the minimum information required to create a two-...
3
votes
1answer
186 views

For which chess boards do solutions exist for this generalised Knight's Tour problem?

We know from a theorem by Schwenk that for any (m x n) chess board with $m \leq n$ it is always possible to create a knight's tour unless one or more of these three conditions are met: m and n are ...
2
votes
2answers
414 views

Putnam 2001 - Problem A-1 (On a binary operation)

Let $*$ be a binary operation acting on a non-empty set $S$, such that $$(a*b)*a=b,$$ for all $a,b\in S$. Prove that $$a*(b*a)=b,$$ for all $a,b \in S$.
1
vote
2answers
59 views

polynomial series and root multiplicity

Excuse me, because I know this is a double post but I can't for the life of me find the original post. Given a sequence $(a_n)$, one can construct a polynomial of the form $\sum\limits_{n=0}^j(x^na_n)...
0
votes
3answers
117 views

How many persons do you think are liar?

There are 10 person. First person says: At least one of the person is liar. Second person says: At least two of the person is liar. Third person says: At least three of the person is liar. Fourth ...
0
votes
1answer
290 views

Base 12 Versus Base 16

I'm not good when it comes to math, so forgive me. I'm doing a personal study of is there a better base number for our culture to use? I have to consider factors like: the number of digits to write, ...
0
votes
2answers
91 views

Is There An Alternative To Using 0 As A Placeholder?

I'm no math wiz here, but I have a question that I can't wrap my head around. In fact, I don't even know how I would even go about asking the question properly. Is there an alternative to using 0 as a ...
7
votes
2answers
181 views

Mental Arithmetic

This is very possibly not the best place to ask this, however it's the best I could find but please suggest anywhere else that might be better suited. I'm building a sort of challenge revolving ...
14
votes
3answers
8k views

The Best Strategy and Highest Possible Score for the “Threes!” Game.

[There's still the strategy to go. A suitably robust argument that establishes what is statistically the best strategy will be accepted.] Here's my description of the game: There's a $4\times 4$ ...
1
vote
3answers
177 views

What is the next number? [closed]

What is the next number in the following set ? $$1,11,21,1211,111221, \ldots$$
4
votes
1answer
94 views

Is there any way to analyze an absurdly large exponent?

On a recent Giant Bombcast, someone wrote in and asked an absurd question (as is usual for this podcast). In short, the question was: Given a 1080p TV, how long would it take to view every ...
0
votes
0answers
56 views

Integral of a function and its inverse

This comes from the comments section of this question. The original question was to show the following identity for some increasing invertible function $f$ $$\int_{a}^{b}f(x)\,dx+\int_{f(a)}^{f(b)}f^...
46
votes
1answer
1k views

How likely is it not to be anyone's best friend?

A teenage acquaintance of mine lamented: Every one of my friends is better friends with somebody else. Thanks to my knowledge of mathematics I could inform her that she's not alone and $e^{-1}\...
0
votes
1answer
72 views

Degree sequence in $O(n)$

How can we determine the whether a sequence of non negative integers is a valid degree sequence in $O(n)$. I have determined an $O(n\log n)$ algorithm using erdos-gallai theorem.
1
vote
1answer
140 views

NCAA bracket and binomial coefficients

Given that March Madness is almost here I was trying to figure out the probability of constructing a perfect bracket if you just flipped a coin for every game. I came up with two possible solutions. ...
-1
votes
1answer
154 views

Question on Speed and Distance

X, Y and Z move along a circular path of length 1.2 km with speeds of 6 km/h, 8 km/h and 9 km/h respectively. X and Y move in the same direction but Z moves in opposite direction. If they all start at ...
3
votes
1answer
911 views

How can I use math to fill out my NCAA tournament bracket?

With the NCAA basketball tournament right around the corner and the conference tournaments just beginning, it's the perfect time to consider strategies to fill out an NCAA tournament bracket. How can ...
1
vote
0answers
81 views

Describing the sequence A224239.

I've been trying to describe mathematically the $n$th term $a_n$ of the sequence A224239. We get $a_n$ by counting the distinct ways to fill an $n\times n$ grid with squares of smaller integer size, ...
1
vote
1answer
643 views

Cyclic tower of hanoi problem [duplicate]

If I have 3 rods in a circle and it is allowed to move the disks only in the clockwise direction. How many moves is necessary to move n disks from first rod to the third rod?
1
vote
1answer
67 views

$[x-\frac{1}{n}, (n-1)x+\frac{1}{n}]$ contains an integer $\forall x\in \mathbb{R}$ and $\forall n\in \mathbb{N}$

For any real number x: Prove that among the numbers x,2x,...,(n-1)x ,there is one that differs from an integer by at most $\frac{1}{n}$. any hints for a pigeon solution. Non-pigeon solution ...
1
vote
1answer
124 views

shorter proof of generalized mediant inequality?

Show $\frac{a_{1}+...+a_{n}}{b_{1}+...+b_{n}}$ is between the smallest and largest fraction $\frac{a_{i}}{b_{i}}$, where $b_{i}>0$. Attempt Assume the largest is $\frac{a_{n}}{b_{n}}\Rightarrow$ ...
4
votes
2answers
184 views

Evaluate $\sum_0^\infty \frac{1}{n^n}$

Courtesy of this xkcd comic I now know that $$ \sum_{n=1}^\infty \frac{1}{n^n} \approx \ln^e(3) $$ Echoing the views of the comic itself, if I ever find myself taking $\ln^e(x)$ then something has ...
2
votes
1answer
162 views

Guests at a table

Fifteen chairs are evenly placed around a circular table. On the table are the name cards of fifteen guests. After the guests sit down, it turns out that none of them is sitting in front of his own ...
2
votes
1answer
84 views

Ping Pong players

A and B play ping pong game multiple times. The person serving first has a probability p of winning that game. A serves the first game and thereafter the loser serves first. If p(n) = pbt that A ...
10
votes
2answers
223 views

Prove $\sum_{n=1}^\infty(e-\sum_{k=0}^n\frac1{k!})=1$

This comes from the comments section of this question here, credits Lucian. The statement is $$\sum_{n=1}^\infty\left(e-\sum_{k=0}^n\frac1{k!}\right)=1$$ This looks really interesting, so I was ...