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

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25
votes
4answers
1k views

Which is bigger?

In my classes I sometimes have a contest concerning who can write the largest number in ten symbols. It almost never comes up, but I'm torn between two "best" answers: a stack of ten 9's (exponents) ...
1
vote
2answers
501 views

Determining odds in Blackjack?

How do you determine the different odds in Blackjack? For example, what would be the difference in odds from using 1, 2, or 3 decks? Also, what would be the difference in odds if you shuffle the deck ...
1
vote
1answer
71 views

Knowing the time of arrival to point X

I have a bus that does A-------X------------------------B it goes at 10 hours from A, having: Speed at A sA = 10 m/s constant ...
17
votes
5answers
763 views

Fun math outreach/social activities

What are some great math social activities for students? I'm looking for things that bring people together with a "light" mathematical touch. The goal is to create a stronger mathematical community in ...
5
votes
4answers
982 views

Question about basic strategy in Blackjack

I was watching Beating Blackjack with Andy Bloch where he runs through the basic strategy charts that outline the best strategy with playing the game. Later he also talks about the methodologies to ...
15
votes
9answers
23k views

When the roulette has hit 5 reds why shouldn't I bet to black?

First some context, I'm not a mathematician, not even close (as you will soon see) I do grasp some things about it but in a need to know basis, so plain english answers are appreciated (too). I can't ...
23
votes
1answer
1k views

Going to the Movies!

I was looking at movie times today and was struck by the oddly-spaced showing times. For example, at the local Loew's Theater "Tron: Legacy 3D" (127 min.) is playing on two screens at the following ...
0
votes
1answer
554 views

Units of Hamming, and Euclidean distance

This is just a simple doubt I wanted to clear. I'm calculating the Hamming and Euclidean distance between two columns in a matrix, where each column is storing time information in seconds of when a ...
11
votes
3answers
3k views

Lights out game on hexagonal grid

I greatly enjoyed the Lights Out game described here (I am sorry I had to link to an older page because some wikidiot keeps deleting most of the page). Its mathematical analysis is here (it's just ...
5
votes
1answer
755 views

Can somebody explain the plate trick to me?

I learned of the plate trick via Wikipedia, which states that this is a demonstration of the fact that SU(2) double-covers SO(3). It also offers a link to an animation of the "belt trick" which is ...
28
votes
7answers
2k views

Quotient geometries known in popular culture, such as “flat torus = Asteroids video game”

In answering a question I mentioned the Asteroids video game as an example -- at one time, the canonical example -- of a locally flat geometry that is globally different from the Euclidean plane. It ...
5
votes
3answers
575 views

How many ways can I make six moves on a Rubik's cube?

I am writing a program to solve a Rubik's cube, and would like to know the answer to this question. There are 12 ways to make one move on a Rubik's cube. How many ways are there to make a sequence of ...
-2
votes
3answers
3k views

How to solve number series with $f(n) = n^2 + 1$

Let's say I have this series of numbers 2, 5, 10, 17. Now somebody told me that next number is 26. He used this function for that: ...
2
votes
1answer
610 views

A problem related to the number 1963

You are allowed to use +, -, / and * (plus, minus, division and multiplication) signs and bracketing. These signs you can put between the numbers 1963 to form mathematical expressions. You must put ...
8
votes
1answer
422 views

$\binom{n}{k} : \binom{n}{k+1} : \binom{n}{k+2} = a : b : c$

It is a rather surprising fact (to me, at least) that $\displaystyle \binom{14}{4} = 1001$; $\displaystyle \binom{14}{5} = 2002$; $\displaystyle \binom{14}{6} = 3003$. Actually, this is the only ...
3
votes
2answers
184 views

Five Fridays and Sundays on October

How to prove that if you take any 400 consecutive Octobers then exactly 14 % of those years have five Fridays and Sundays?
4
votes
2answers
302 views

How is done the calculation of the minimum number of movement to solve any configuration of Rubik's Cube?

I have read a few weeks ago that some mathematical researchers have discover that the minimum number of movements to solve any initial configuration of a Rubik's cube has been downsized to 20. How do ...
9
votes
1answer
562 views

How many disconnected graphs of the Rubik's cube exist?

Let us say that a Rubik's cube in a particular configuration is in a particular "state". All other configurations of this cube (other "states"), which can be achieved by rotations of the cube can be ...
4
votes
3answers
2k views

Formula(/How) to find 2 numbers that add together to give one number and times to give another

I have 2 numbers (a & b) but I need a formula (or a how to) to find which 2 numbers (c & d) will add together to give a and times together to give b. So ...
11
votes
1answer
678 views

What's the probability that a sum of dice is prime?

Prompted by today's Minute Math question on the MAA site (http://amc.maa.org/mathclub/5-0,problems/T-problems/T-web,ia/2005web/tb05-12-ia.shtml), I started thinking about the probability that the sum ...
4
votes
2answers
322 views

a sequential game of dice

consider the following game: 10 dice are tossed and those showing 3 are more are retained. [those showing 2 or less are discarded.] the remaining dice are tossed again and those showing 4 or more are ...
5
votes
1answer
544 views

Interesting Taxicab Problem?

I came up with this problem after discussion of taxicab geometry in math class... I thought it was a simple problem, but still pretty neat; however, I am as of yet unsure of whether my answer is ...
3
votes
2answers
807 views

Is this version of the Hanoi towers problem NP-complete?

This was really inspired by Solitaire, but a few people reacted with ``oh, it's like the towers of Hanoi, isn't it?'' so I'll try to pose the problem in terms of discs here. Let's start. There are n ...
6
votes
2answers
330 views

Watchdog Problem

I just came up with this problem yesterday. Problem: Assume there is an important segment of straight line AB that needs to be watched at all time. A watchdog can ...
27
votes
6answers
3k views

Where is the flaw in this argument of a proof that 1=2? (Derivative of repeated addition)

Consider the following: $1 = 1^2$ $2 + 2 = 2^2$ $3 + 3 + 3 = 3^2$ Therefore, $\underbrace{x + x + x + \ldots + x}_{x \textrm{ times}}= x^2$ Take the derivative of lhs and rhs and we get: ...
-2
votes
4answers
2k views

Interesting numbers in Maths [closed]

Mathematics is beautiful. Many numbers are interesting such as 1729 = 13 + 123 = 93 + 103 Please list out the interesting numbers and reasons to make number interesting
6
votes
3answers
2k views

Optimal Strategy for Deal or No Deal

When I have watched Deal or No Deal (I try not to make a habit of it) I always do little sums in my head to work out if the banker is offering a good deal. Where odds drop below "evens" it's easy to ...
48
votes
5answers
8k views

Logic problem: Identifying poisoned wines out of a sample, minimizing test subjects with constraints

I just got out from my Math and Logic class with my friend. During the lecture, a well-known math/logic puzzle was presented: The King has $1000$ wines, $1$ of which is poisoned. He needs to ...
7
votes
3answers
2k views

Which books would you recommend about Recreational Mathematics?

By this I mean books with math puzzles and problems similar to the ones you would find in mathematical olympiads.
40
votes
6answers
4k views

How come $32.5 = 31.5$?

Below is a visual proof (!) that $32.5 = 31.5$. How could that be?