## Search found 206 matches

Tue Dec 18, 2012 1:14 am UTC
Forum: Logic Puzzles
Topic: Create a perfect lossless compression algorithm
Replies: 21
Views: 5161

### Re: Create a perfect lossless compression algorithm

dudiobugtron wrote:However, there is one extra piece of information they can transmit, and that is what was sent in the previous file. Is there any way they can use this to their advantage?

No, because
jestingrabbit wrote:no matter what they do, they have to have a pairing between all 2^(2^20) files and their possible messages
Thu Dec 13, 2012 7:03 pm UTC
Forum: Logic Puzzles
Topic: Cypher with Some Known Plaintext
Replies: 6
Views: 3777

### Re: Cypher with Some Known Plaintext

Explanation of difference analysis: The classical way to crack a Vigenere cipher is by looking at pairs of identical letters in the ciphertext. If there's a pair of identical letters 35 letters apart, that's weak evidence for the key length being 5 or 7 (or 1 or 35). This has to do w...
Sat Nov 24, 2012 2:19 pm UTC
Forum: Logic Puzzles
Topic: New abstract game : Invasion
Replies: 7
Views: 3238

### Re: New abstract game : Invasion

Player 1 (red) does this strategy, picking a random valid hex if the hex required is NaN or already occupied. What if there aren't any valid hexes left? This would occur when, in Player 2's hypothesized winning strategy, Player 2 has exactly one valid play (say, spot A) before getting stuck. In the...
Tue Sep 11, 2012 1:35 am UTC
Forum: Coding
Topic: program not working as expected
Replies: 5
Views: 1815

### Re: program not working as expected

You know, instead of pasting lots of identical lines, you can just use a loop: def lt(): #Whatever "lt" is supposed to stand for for i in xrange(10000): loop() Also, as Xanthir said, I'd be much more inclined to look over this if you gave us an idea of how your code is supposed to work in ...
Thu Jun 28, 2012 2:48 pm UTC
Forum: Mathematics
Topic: Deterministic biased sampling without replacement
Replies: 2
Views: 982

### Re: Deterministic biased sampling without replacement

Maybe you can model the infinitely many balls as something like this: There's one big mixed-up black-and-white soup. You're going to drink x fraction of the soup total. At each instant, if the fraction of white left in the soup is w, your drink will contain (1+b)w/((1+b)w + 1-w) fraction of the whit...
Sun May 13, 2012 2:46 pm UTC
Forum: Fit Club
Topic: Run 10,000 miles
Replies: 1340
Views: 311064

### Re: Run 10,000 miles

6434.4 + 3.1 = 6437.5

Just ran the most horrible 5K of the year. "hill" is only one letter away from "hell".
Sun May 13, 2012 2:13 am UTC
Forum: Forum Games
Topic: 3 letters in a word
Replies: 1795
Views: 278967

### Re: 3 letters in a word

mithril

yru
Sun May 15, 2011 4:11 am UTC
Forum: Mathematics
Topic: Poisson Distributions- tricky problem
Replies: 1
Views: 645

### Poisson Distributions- tricky problem

A friend and I were studying for an exam, and in the practice problems we came across this: "X and Y are independent Poisson random variables with E(X)=E(Y)=1. Find E(X 2 |X+Y=m)." I eventually solved it like so: We want to evaluate the sum as i goes from 0 to m of: P(X=i)*P(Y=...
Wed Mar 02, 2011 4:22 am UTC
Forum: Mathematics
Topic: problem deriving a geometric formula
Replies: 2
Views: 495

### Re: problem deriving a geometric formula

If you just plain algebra-ize the last equation you had in the document to solve for dr, you should get

dr = SQRT( r02l0/(l0+dl) ) - r0

Taking the r02 out of the square root and factoring out an r0 from the resulting expression should give you the formula you wanted.
Tue Feb 22, 2011 9:53 pm UTC
Forum: Mathematics
Topic: Problems that seem difficult but aren't
Replies: 75
Views: 8725

### Re: Problems that seem difficult but aren't

Prove that, for any n>0, the numbers n+2 and n^2+n+1 cannot simultaneously be perfect cubes.
Thu Feb 10, 2011 12:15 am UTC
Forum: Mathematics
Topic: Problems that seem difficult but aren't
Replies: 75
Views: 8725

### Re: Problems that seem difficult but aren't

Here's a fun one:

A continent is divided into several countries, none of which are landlocked. Prove that the map of countries can be 3-colored such that no two bordering countries have the same color.
Tue Feb 01, 2011 10:34 pm UTC
Forum: Mathematics
Topic: Fun Math Riddles
Replies: 54
Views: 6312

### Re: Fun Math Riddles

Kirby, yes, it's possible to do even better!
Tue Jan 11, 2011 4:31 am UTC
Forum: Mathematics
Topic: Potato Chip Theorem- What's the real name?
Replies: 20
Views: 3133

### Re: Potato Chip Theorem- What's the real name?

@Dopefish: Yeah, that's the proof I had heard too. I don't think the boundary of the potato chip is always a plane, though. (i.e. a cubical potato and a spherical potato will make this weird shape: http://www.autodeskpress.delmar.cengage.com/resources/olcs/acad2000/oct02/boolean%20-%203.gif Looks mo...
Tue Jan 11, 2011 2:06 am UTC
Forum: Mathematics
Topic: Potato Chip Theorem- What's the real name?
Replies: 20
Views: 3133

### Potato Chip Theorem- What's the real name?

A while ago I heard a puzzle that went like so: You have two potatoes. Prove you can slice one potato chip from each one such that the resulting chips have exactly the same size and shape. Apparently this is a result in topology, and one with a very nice proof at that, but after fierce Googling I ha...
Sat Dec 04, 2010 2:26 am UTC
Forum: Forum Games
Topic: Counter-factuals
Replies: 47
Views: 6675

### Re: Counter-factuals

If crops could be grown on seawater alone without affecting the taste, water-plentiful fruits like watermelons and strawberries would become vastly more available than (for example) potatoes and avocados. Thus, the most selective delicacy of the pastry world will be the water-deprived chocolate soda...
Wed Nov 03, 2010 8:58 pm UTC
Forum: Logic Puzzles
Topic: To make a touchdown (American football)
Replies: 9
Views: 3277

### Re: To make a touchdown (American football)

We need 8 first downs, giving us (4/5)^8 or roughly 16.8% chance of getting a touchdown. We can do better than this (more than 20%!) with just the first play. 1/5+epsilon chance of going 80 yards ahead, 4/5-epsilon chance of going 20 yards back. (where epsilon=whatever it needs to be for the expect...
Sat Oct 30, 2010 6:14 pm UTC
Forum: Logic Puzzles
Topic: Interesting Chess Problem
Replies: 17
Views: 5072

### Re: Interesting Chess Problem

(ways of promoting 4 pawns)

I count 5.
...and gets mated next move.

Also, in the situation in the video at least, there were two ways of mating on the last move.
Wed Oct 13, 2010 9:43 pm UTC
Forum: Mathematics
Topic: Taking out pairs from a deck of cards...
Replies: 13
Views: 1656

### Re: Taking out pairs from a deck of cards...

Alright, so what's the probability that each pair comes out as a same-colour pair? I know that for 4 cards (1 kind), it's 1 in 3... And whether the cards come out in same-color pairs is independent for each value, so it's (1/3)^n. Edit: And the deck doesn't have to be cleared in one go, either. By ...
Thu Oct 07, 2010 9:59 pm UTC
Forum: Mathematics
Topic: Taking out pairs from a deck of cards...
Replies: 13
Views: 1656

### Re: Taking out pairs from a deck of cards...

As for the other question, how often can a deck be fully emptied: Let's say there are only two values in the deck. Then a deck like 12221121 can be cleared, but a deck like 12121212 cannot. In general, given a random positioning of 2s amongst the 1s, working out the probabilities there's a ~.514 cha...
Sat Oct 02, 2010 2:01 am UTC
Forum: Logic Puzzles
Topic: Factorial Properties
Replies: 15
Views: 3509

### Re: Factorial Properties

Spoiler:
(Array.new(n) {|x| x+1}).inject(1) {|product, new| product*new}.to_s.gsub(/[0]+\z/) {|match| puts match.length}

Computes the factorial, converts it to a string, and finds the number of zeroes at the end.
Sat Oct 02, 2010 1:12 am UTC
Topic: 0245: "Floor Tiles"
Replies: 252
Views: 69963

### Re: "Floor Tiles" Discussion

I do a bunch of the stuff earlier posters have mentioned, and a lot of them I didn't even realize I do before reading them. Here's a few more: After I finish a multiple choice test, I start at the last question on the sheet and jump up to the top, using filled-in answers as platforms. Valid jumps ar...
Sat May 29, 2010 9:46 pm UTC
Forum: Logic Puzzles
Topic: How to confirm if someone is your "future you"?
Replies: 96
Views: 14869

### Re: How to confirm if someone is your "future you"?

The "Think of a random number on the spot" approaches only work with a stable-loop-type version of time travel. If you split into another copy of the universe when you go back in time, you'll be stuck. My method is, I have a password usable for any of these sorts of situations. I've never ...
Fri Mar 19, 2010 11:20 pm UTC
Forum: Logic Puzzles
Topic: Bird-Bear-Book Puzzle
Replies: 6
Views: 1931

### Re: Bird-Bear-Book Puzzle

Yep, you've got it.
Thu Mar 18, 2010 1:59 am UTC
Forum: Logic Puzzles
Topic: Bird-Bear-Book Puzzle
Replies: 6
Views: 1931

### Bird-Bear-Book Puzzle

My friends and I made this up at school- it's a combination of ~3 other puzzles we saw in various places. The bird the cat the dog the boy the woman that brought the book the kid wanted to be read to out of about down under up for a story hugged owned chased ate died. What color is the bear? You can...
Thu Mar 11, 2010 1:19 am UTC
Forum: School
Topic: Stupid mistakes on Tests.
Replies: 51
Views: 5925

### Re: Stupid mistakes on Tests.

On a recent Calc test:

9+12=105

Wha-a...? How did I manage that?
Wed Mar 10, 2010 1:20 am UTC
Forum: Logic Puzzles
Topic: Take out the cycles
Replies: 4
Views: 1803

### Re: Take out the cycles

Yep, you've basically solved the first part. Tirian's idea is the key.
Tue Mar 09, 2010 9:16 pm UTC
Forum: Logic Puzzles
Topic: Take out the cycles
Replies: 4
Views: 1803

### Take out the cycles

Start with 8 points, and connect all possible edges between the points. That is, make a complete graph of order 8. On each step, you are allowed to remove an edge if it's part of a cycle with length 7. Is it possible to keep removing edges until no cycles are left in the graph? In general, is it pos...
Thu Mar 04, 2010 2:30 am UTC
Forum: Mathematics
Topic: lim(n!)^(1/n) as n->inf
Replies: 6
Views: 10790

### Re: lim(n!)^(1/n) as n->inf

(log1 + log2 + ... + logn)/n

=(log1 + log2 + ... + log(n/2))/n
+ (log(n/2+1) + log(n/2+2) + ... + logn)/n

What happens if you plug in 2ea for n?
Tue Mar 02, 2010 12:30 am UTC
Forum: Coding
Topic: Matching any number in an array?
Replies: 15
Views: 1751

### Re: Matching any number in an array?

if(iNum[i] != <AnyNumberInArray>) I don't know much about java, but will this work? Numcheck = 1 for (j=0; j>iNum.size; j++){ //I don't know what Java's size function is, but this checks every element in the array if(iNum[i] == iNum[j]){Numcheck = 0} //set it to 0 if it matches the number } and the...
Mon Mar 01, 2010 11:03 pm UTC
Forum: Mathematics
Topic: Calculator Hacking
Replies: 8
Views: 2824

### Re: Calculator Hacking

Today I fiddled with huge matrices to get my TI-89's available memory down to 3 bytes.
You can only type 3 characters onto the screen now, and it gives a memory error when computing 1+1.
Me and my friends were joking about handing these out for the SAT's.
Mon Mar 01, 2010 10:55 pm UTC
Forum: Forum Games
Topic: The Intersecting Geekeries Test
Replies: 9
Views: 1874

### Re: The Intersecting Geekeries Test

I liked it. Got 20/25, but then again I've never watched Star Trek or Buffy. The final question was a little too easy, I figured it out just from the first two terms :wink: . Although, maybe I'm just being stupid, but in the "m lights n lights" question (#17), isn't it m=4 and n=5? 4 /= 5 ...
Sat Feb 06, 2010 8:33 pm UTC
Forum: Logic Puzzles
Topic: The Bobs
Replies: 37
Views: 4960

### Re: The Bobs

I have a solution with only one extra Bob, but everyone's age is in months and most of them are less than 1 year old. I don't think that's how it's supposed to work out, but with the 2/4/9 month differences and the "Bob is 3x Bob's age" I don't see how it's possible otherwise. Also, I thin...
Sun Jan 24, 2010 6:36 pm UTC
Forum: Logic Puzzles
Topic: 2 puppies
Replies: 132
Views: 18440

### Re: 2 puppies

I agree with the 1/3 for the puppy problem, but my math teacher asked our class this recently: You know a woman who has two children, but you don't know what gender they are. One day you see her in a toy store buying a doll, which you conclude is a present for her daughter. What is the probability t...
Wed Dec 23, 2009 9:00 pm UTC
Forum: Coding
Topic: TI-84 basic help
Replies: 4
Views: 855

### Re: TI-84 basic help

Did you clear the list before running the program?
Does it work if you go up to 20 instead of 1000?
Tue Dec 22, 2009 3:44 pm UTC
Forum: Coding
Topic: M-Set in Python
Replies: 4
Views: 747

### Re: M-Set in Python

I made a version of that where it made a tiny M set and then made it twice as big each step, only testing squares on the boundary. It was pretty fast; it actually made a reasonably sized picture on my TI-84 in a couple of minutes.
Sun Dec 13, 2009 5:40 pm UTC
Forum: Mathematics
Topic: Snail on a string
Replies: 4
Views: 1142

### Re: Snail on a string

Instead of stretching the rubber band to X times the size,
Spoiler:
why not shrink the snail to 1/X times the size? It's the same thing, really, you just shrunk space.
Then the snail's speed at time t seconds is 1/t (cm/s), and you can use calculus to find the answer.
Sun Dec 13, 2009 4:31 pm UTC
Forum: Mathematics
Topic: Numerical Integration Question
Replies: 2
Views: 459

### Numerical Integration Question

Usually in numerical integration you have a bunch of pairs (x,f(x)) and you have to find the approximate integral of the function. What would you do if you instead had a bunch of triplets (x,f(x),f'(x))? Would it be simplest just to put cubic polynomials between consecutive points? How accurate woul...
Fri Dec 11, 2009 11:59 pm UTC
Forum: Music
Topic: What are you listening to?
Replies: 9561
Views: 1166149

### Re: What are you listening to?

t=Node- Border of Life
You too, modularblues?
Wed Dec 09, 2009 1:09 am UTC
Forum: Logic Puzzles
Topic: brain in a vat
Replies: 214
Views: 26161

### Re: brain in a vat

If it's using the "Prefect AI", then a really long message like: -R---890-6b-b=wge90-nyw -e---7The cat is happy today -s---1How are you?? Hello -p---7Gosh, I hope it doesn't -o---5rain, or the party will be -n---5canceled, so I'll have -d---3to buy a new umbrella ------1and hopscot...
Tue Dec 01, 2009 1:54 am UTC
Forum: Mathematics
Topic: A Probability Question (3D random walk)
Replies: 6
Views: 1808

### Re: A Probability Question (3D random walk)

The total probability should be a triple summation for k=x to n ,l=y to n and m=z to n; Huh, this is leaving me wondering whether there's a way to do this without any summations at all. It's definitely possible for the 2-dimensional case. Interestingly, it's also possible for the 4-dimensional case...