Search found 72 matches

by Lothar
Fri Mar 20, 2015 9:56 pm UTC
Forum: Mathematics
Topic: Graph Theory definition question
Replies: 6
Views: 1917

Re: Graph Theory definition question

I've heard this called the degeneracy of a graph. I'm not sure what it has in common with treewidth, other than the fact that trees have treewidth 1 and are 1-degenerate.
by Lothar
Sat Jan 10, 2015 3:38 pm UTC
Forum: Logic Puzzles
Topic: Filomino puzzle
Replies: 4
Views: 2787

Re: Filomino puzzle

Can you check your solution for the max 9 puzzle? I believe there's no solution: Adding up all of the polyomino areas in the most conservative way (by assuming that matching numbers share polyominoes if possible) gives 120, so there is at most 1 unhinted polyomino. There's no way to spl...
by Lothar
Mon Jun 24, 2013 6:17 pm UTC
Forum: Logic Puzzles
Topic: Test-solve my puzzles, please
Replies: 174
Views: 59688

Re: Test-solve my puzzles, please

Hi ArDeeJ, these were all really fun. Exactly the right difficulty for me at the moment. Challenging, but not frustrating.

I'm pretty sure the solutions have all been unique, since I used deduction throughout (though I might have made a mistake somewhere). Very nice puzzles!
by Lothar
Mon Apr 30, 2012 3:24 pm UTC
Forum: Coding
Topic: noob python and C questions
Replies: 42
Views: 10254

Re: noob python questions

Indeed, memoization seems to be what you want to do. Another way is for example:

Code: Select all

def fib(n, mem = {0:0, 1:1}):
    if n in mem:
        return mem[n]
    mem[n] = fib(n - 1) + fib(n - 2)
    return mem[n]
by Lothar
Fri Jan 13, 2012 6:01 pm UTC
Forum: Mathematics
Topic: Algebra I: Quadratics, Algebra Tiles, and a weird result
Replies: 9
Views: 2187

Re: Algebra I: Quadratics, Algebra Tiles, and a weird result

eventhorizon82 wrote:For [imath]x^2 + 7x + 6[/imath] factoring into [imath](x+3)(x+2)[/imath]

Nitpick: Those aren't quite the same quadratic...
by Lothar
Fri Jan 13, 2012 5:54 pm UTC
Forum: Mathematics
Topic: Help a philosophy student with some math about possibilities
Replies: 16
Views: 2341

Re: Help a philosophy student with some math about possibili

Obviously there are k_n possibilities from the first n symbols. This covers all the cases in which the closing bracket is not after the n+1th symbol. There are another n+1 possibilities in which the closing bracket is after the n+1th symbol (Because the opening bracket can start in front of any sym...
by Lothar
Fri Dec 02, 2011 6:36 pm UTC
Forum: Mathematics
Topic: "Surreal numbers" or "when 0.999... ≠ 1 etc."
Replies: 13
Views: 5807

Re: "Surreal numbers" or "when 0.999... ≠ 1 etc."

Right, but convergence is a useless concept in the surreals, as the natural (order) topology is the discrete topology. Not quite sure I believe this. I'm under the impression that every non-empty open interval contains infinitely many surreal numbers (so no finite sets are open, save the empty set)...
by Lothar
Tue Nov 15, 2011 4:13 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0977: "Map Projections"
Replies: 353
Views: 139584

Re: 0977: "Map Projections"

The comic prompted me to do some research into map projections, and I fell in love with the Werner projection, which is as of now my favorite. Haven't even seen it get mentioned in the thread so far. :cry:
by Lothar
Mon Oct 31, 2011 8:41 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 92955

Re: "Oh no! We forgot how to say... math... stuff!"

One thing that I have found annoying is that the radix point is a point at the bottom of the line, where it can easily be missed; this leads to "protections" like "0.34" in order to prevent that from being read as "34"; a number less that .1 must start with a "0&q...
by Lothar
Fri Jul 01, 2011 12:02 am UTC
Forum: Mathematics
Topic: A set in the complex plane edit: ?s about complex variables
Replies: 26
Views: 3540

Re: A set in the complex plane edit: ?s about complex variab

Firstly, in question 6, I'm interpreting " f(G) is a subset of the unit circle" to mean \{f(z)|z \in G \} \subset \{z: |z|=1 \} , and I'm not sure if that's correct or not (to be clear, I dunno exactly what it means to take the function of a region -- I've never encountere...
by Lothar
Thu Jun 09, 2011 10:25 am UTC
Forum: Forum Games
Topic: Type the Sentence: No Backspace, No Peeking
Replies: 461
Views: 98163

Re: Type the Sentence: No Backspace, No Peeking

i et you canpt type thid drnyxxt buyybkkuiu

HA! Success!
by Lothar
Mon Mar 28, 2011 12:50 pm UTC
Forum: Logic Puzzles
Topic: Partitioning A Formula
Replies: 10
Views: 2706

Re: Partitioning A Formula

Not so difficult... a bit of case analysis. Perhaps someone can come up with a better method? There is no solution. Clearly each son must have at least one part, for if one son didn't, then according to requirements, he and two other sons should have all of the parts among them, but as he is red...
by Lothar
Fri Jan 21, 2011 2:44 pm UTC
Forum: Mathematics
Topic: Binary fractal
Replies: 14
Views: 2037

Re: Binary fractal

You might want to check your code... I get a slightly different curve, following your instructions. For example, my n = 4 curve looks as follows:

binaryfractal4.png
binaryfractal4.png (2.2 KiB) Viewed 1636 times
by Lothar
Thu Jan 20, 2011 10:33 am UTC
Forum: Mathematics
Topic: Nerd alert (messing around with the quadratic formula)
Replies: 25
Views: 2979

Re: Nerd alert (messing around with the quadratic formula)

No, I know about imaginary roots of a quadratic always coming in complex conjugate pairs, this was showing how the coefficients (such as the a, b and c in ax^2+bx+c=0) affect what the imaginary root will be and it turned out that either the c or the b didn't matter. It's pretty clear from the quadr...
by Lothar
Wed Jan 19, 2011 9:31 am UTC
Forum: Logic Puzzles
Topic: Bloxorz optimal path
Replies: 26
Views: 11613

Re: Bloxorz optimal path

Qaanol wrote:I’d like to see your solutions please.


PM sent. :)
by Lothar
Thu Nov 25, 2010 10:09 pm UTC
Forum: Mathematics
Topic: Coin Probability Question
Replies: 7
Views: 2059

Re: Coin Probability Question

Spots wrote:But, isn't it 50%?
You know one of them is heads. The other can be heads or tails, the probability for either case being 50%.

Ah, but you don't know which one. If you flip two coins, getting one heads and one tails is twice as likely as getting two heads.
by Lothar
Sun Nov 21, 2010 8:09 pm UTC
Forum: Mathematics
Topic: Dream Equation
Replies: 15
Views: 1888

Re: Dream Equation

If the map is one-to-one that would seriously limit the number of solutions. But without any such restrictions you will find there are a whole lot of them. In fact, there is a unique one-to-one function T: R -> R which satisfies the equation, as was pointed out by sagekilla. There is a unique inver...
by Lothar
Thu Sep 16, 2010 8:27 pm UTC
Forum: Mathematics
Topic: The Odd Party Conjecture
Replies: 25
Views: 3778

Re: The Odd Party Conjecture

So you have a connected graph with an even number of vertices. You want to know if it is always possible make all vertices have odd degree by removing edges from the graph. That's not how I interpreted the problem. I thought he has a connected graph on an even number of vertices, and wants to parti...
by Lothar
Fri Aug 13, 2010 11:59 pm UTC
Forum: Forum Games
Topic: Where in the World...
Replies: 1129
Views: 114767

Re: Where in the World...

Agree to north of the Shonai River (= brown line).
by Lothar
Tue Aug 10, 2010 4:31 am UTC
Forum: Forum Games
Topic: Where in the World...
Replies: 1129
Views: 114767

Re: Where in the World...

Agree to Hong Kong or Japan.

Also, Hi!
by Lothar
Tue Jul 27, 2010 8:35 am UTC
Forum: Logic Puzzles
Topic: Cat and mouse
Replies: 29
Views: 13946

Re: Cat and mouse

Indeed, quite a fun one! The cat can also try 2, 2, 4, 4, 4, 2. If the mouse is in 1 or 2, the cat will catch it in the first two tries. After this, the mouse is in 3, 4, or 5. If it is in 4 or 5, the next two 4's will catch it. So the mouse must have been on 3 after the first two tries to survi...
by Lothar
Wed Jun 09, 2010 7:35 pm UTC
Forum: Coding
Topic: Manufactoria - Make Turing Machines with Conveyor Belts
Replies: 350
Views: 126601

Re: Manufactoria - Make Turing Machines with Conveyor Belts

Slowest level 1? ?lvl=1&code=c12:6f2;c13:6f1;c13:5f2;c14:5f3;c14:6f3;c14:7f0;c13:7f0;c12:7f0;c11:7f1;c11:6f1;c11:5f0;c10:5f3;c10:6f3;c10:7f3;c10:8f3;c10:9f2;c11:9f1;c11:8f2;c12:8f2;c13:8f2;c14:8f3;c14:9f0;c13:9f0; How about this: ?lvl=1&code=i12:6f1;i13:6f0;c13:5f2;c14:5f3;c14:6f0;i11:6f6;c...
by Lothar
Sun May 30, 2010 4:47 am UTC
Forum: Coding
Topic: Manufactoria - Make Turing Machines with Conveyor Belts
Replies: 350
Views: 126601

Re: Manufactoria - Make Turing Machines with Conveyor Belts

Ephphatha wrote:I'm not entirely sure what judiciary is actually asking for. Are we meant to accept palindromes? Strings where the middle two elements are the same?

Strings that are composed of two identical strings in a row, such as RBBRBB.
by Lothar
Sun May 30, 2010 2:28 am UTC
Forum: Coding
Topic: Manufactoria - Make Turing Machines with Conveyor Belts
Replies: 350
Views: 126601

Re: Manufactoria - Make Turing Machines with Conveyor Belts

That's neat, enne. Your solution gave me some tips I could use on mine, and it came out to 102 parts, and after a bit more optimization, I got it down to only 74 parts! ?lvl=31&code=g12:2f3;c6:4f2;c6:5f1;c6:6f1;c6:7f1;c6:8f1;c6:9f1;c6:10f1;c7:4f2;c7:6f3;c7:7f2;r7:8f0;b7:9f1;c7:10f0;g8:3f2;i8:4f4...
by Lothar
Thu May 27, 2010 1:41 am UTC
Forum: Coding
Topic: Manufactoria - Make Turing Machines with Conveyor Belts
Replies: 350
Views: 126601

Re: Manufactoria - Make Turing Machines with Conveyor Belts

I'm not really sure how to implement carrying for Officers (adding 1 to a binary string). Hint: You can use the same algorithm to add 1 to higher place values, if you can find a way to delimit where you've already added. Hint 2: Put a red in front of the string at the beginning, so you can carr...
by Lothar
Wed Feb 03, 2010 11:00 am UTC
Forum: Mathematics
Topic: A problem with Gaussian curvature
Replies: 1
Views: 519

Re: A problem with Gaussian curvature

One way to do it is to find a sphere containing the surface, then shrinking the sphere until it first touches the surface.
by Lothar
Mon Nov 09, 2009 10:28 pm UTC
Forum: Mathematics
Topic: Question about a descriptive(?) function
Replies: 8
Views: 973

Re: Question about a descriptive(?) function

How about
[math]f(x) = 1 - \frac{1}{x + 1}[/math]
or
[math]g(x) = 1 - e^{-x}[/math]
or
[math]h(x) = 1 - e^{-x^2}[/math]
?
by Lothar
Thu Oct 29, 2009 8:03 am UTC
Forum: Mathematics
Topic: Discontinuous derivative of an explicitly defined function
Replies: 18
Views: 4935

Re: Discontinuous derivative of an explicitly defined function

How about this function: f \left( x \right) = \left\{ \begin{array}{ll} x^2 \sin \left( \frac{1}{x} \right) & \mbox{if } x \neq 0 \\ 0 & \mbox{if } x = 0 \end{array} \right. It is differentiable everywhere, even at 0, as can be checked. But it's derivative is not continuous a...
by Lothar
Fri Oct 23, 2009 7:57 pm UTC
Forum: Mathematics
Topic: Linear Algebra Exam
Replies: 3
Views: 764

Re: Linear Algebra Exam

Can you think of a non-zero polynomial of degree 3 or less, which is sent to 0 by T? If yes, then T is not injective, and hence not invertible.
by Lothar
Sun Oct 18, 2009 9:36 am UTC
Forum: Mathematics
Topic: Limit Superior
Replies: 4
Views: 1583

Re: Limit Superior

I'm also having trouble with an alternate definition of lim sup. It is: If v m =sup{x n : n>=m}, then lim sup X = lim v m . Anyways, the proof used in the book says that this forms a monotone decreasing sequence. And never bothers to explain why? I'm having trouble figuring out why it does. Hapl? B...
by Lothar
Sat Oct 17, 2009 9:46 am UTC
Forum: Logic Puzzles
Topic: Tic Tac Toe With a Twist
Replies: 39
Views: 6153

Re: Tic Tac Toe With a Twist

Analysis of the interesting case: .... .o.. ..x. .... This ends in a draw for any move by X, even passing (by symmetry) given perfect play by both parties. There are 8 moves for X up to symmetry. 1st option: x.. .o. ..x This is a forced draw if O plays on any side, or an X win if O plays in ...
by Lothar
Fri Oct 16, 2009 9:40 pm UTC
Forum: Mathematics
Topic: Why isn't this problem easy? (ants in a box)
Replies: 12
Views: 1374

Re: Why isn't this problem easy?

So you guess walking to the corner, then walking down the edge is fastest. What about walking straight to an edge, then taking the slanted path from the middle of the top edge to the bottom corner of the side face? This gives a length of 2 + \sqrt{2^2 + 4^2} = 2 + 2 \sqrt{5} , which is less than you...
by Lothar
Mon Oct 05, 2009 8:50 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0645: "RPS"
Replies: 185
Views: 51625

Re: "RPS" Discussion

I found it absolutely hilarious. Haven't laughed this much at a comic in a while. Simply brilliant.
by Lothar
Fri May 29, 2009 7:27 am UTC
Forum: Mathematics
Topic: Groups as Permutations
Replies: 12
Views: 1418

Re: Groups as Permutations

Anyway, here is a paper (which I haven't read) related to the question. Presumably, it also has some useful references. Oh, thanks so much! That's very helpful, and seems to be exactly what I'm looking for. Its references look very useful as well. Nice find! Well, the obvious upper bound is the sma...
by Lothar
Thu May 28, 2009 4:34 am UTC
Forum: Mathematics
Topic: Groups as Permutations
Replies: 12
Views: 1418

Re: Groups as Permutations

Since every element of a group is isomorphic to a subgroup of a symmetric group, you can find a matching cycle notation for that element. The element of G with the maximal cycle length sum determines the smallest n for Sn containing G. I'm not sure either, exactly what you mean. Does your first sen...
by Lothar
Thu May 28, 2009 3:40 am UTC
Forum: Mathematics
Topic: Groups as Permutations
Replies: 12
Views: 1418

Re: Groups as Permutations

Thanks, but I'm aware of this... in fact, for a cyclic group of order n = p 1 a 1 ...p k a k , where the p i are all distinct primes, and the a i all positive, we have an element of order n in Sym(p 1 a 1 +...+p k a k ) (think cycle notation), so cyclic groups are no problem (yes, this is also the s...
by Lothar
Thu May 28, 2009 3:13 am UTC
Forum: Mathematics
Topic: Groups as Permutations
Replies: 12
Views: 1418

Groups as Permutations

Hi, I've been reading some abstract algebra books I won as a prize recently, and I'm interested to know something about finite groups, which I have not been able to find easily through Google or Wikipedia. Cayley's Theorem states that every group is isomorphic to a group of permutations. This means ...
by Lothar
Sun Apr 12, 2009 11:42 pm UTC
Forum: Logic Puzzles
Topic: Primrose
Replies: 23
Views: 3239

Re: Primrose

Hmm, I got an opening combo of 14 with 11 spaces:

Spoiler:

Code: Select all

G R B   X B G
B G B R   G R
R   R G B   B
G R   B B R G
B       G   R
R G   R   G B
G B R G B R G


Starting the chain reaction with G at X


I also now hold the highest score :)
by Lothar
Tue Mar 10, 2009 3:38 am UTC
Forum: Mathematics
Topic: combinations that confuse
Replies: 13
Views: 1584

Re: combinations that confuse

It's also the number of solutions to the equation

x1 + ... + xN = N

where the variables xi must all be non-negative integers (think of each xi as counting the occurrences of the i-th color).
by Lothar
Mon Feb 23, 2009 4:15 am UTC
Forum: Mathematics
Topic: Traveling across a square
Replies: 24
Views: 6937

Re: Traveling across a square

is this definition of the limit of a sequence of functions equivalent to one of the definitions you mention? Or is it something completely different and wrong? It's different, but not necessarily "wrong." There are many ways of defining the limit of a sequence of functions. Your definitio...

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