Search found 2058 matches

by jaap
Thu Jun 18, 2015 5:53 am UTC
Forum: Coding
Topic: Happy bases
Replies: 12
Views: 3045

Re: Happy bases

Find a more efficient algorithm to determine whether a number is happy in a given base. One thing I've noticed is that you immediately forget all previous calculations. If you've verified all numbers from 1 to n-1 to be happy, you only need to calculate the sequence for n until reaching any number ...
by jaap
Tue Jun 09, 2015 12:16 pm UTC
Forum: Mathematics
Topic: Independent repeated trials and mutually exclusive events.
Replies: 4
Views: 1635

Re: Independent repeated trials and mutually exclusive event

Mutually exclusive is just a fancy term for saying that there is no overlap between the events. For instance, if I wanted to know the number of people in my class who are either women or math majors, I can't add the number of women to the number of math majors because that would double-count all th...
by jaap
Sat Jun 06, 2015 4:24 pm UTC
Forum: Coding
Topic: Project Euler
Replies: 411
Views: 141537

Re: Project Euler

@jaap: Would you mind referring me to a simple memoized implementation of a factorial method in Java? That would probably help me a lot, just seeing how the memoization is implemented.... Actually, maybe I do know enough to implement it. I suppose you would have to have it in its own class so a fie...
by jaap
Wed Jun 03, 2015 2:53 pm UTC
Forum: Coding
Topic: Reflection around the inside of a circle
Replies: 4
Views: 2784

Re: Reflection around the inside of a circle

I always found it easier to do this kind of thing with vectors, I always make mistakes with trigonometric calculations. And calculating a normal vector for a sphere is really easy. I totally agree. In most languages I've seen, atan2 has the y parameter first, so reflectTangent isn't actually the ta...
by jaap
Tue Jun 02, 2015 10:41 pm UTC
Forum: Mathematics
Topic: Combinations algorithm and property
Replies: 19
Views: 2580

Re: Combinations algorithm and property

The loop part (that the last one is the neighbour of the first one) makes this tricky. Without that part I would solve it by methodically moving freespaces (assuming I didn't misunderstand something). That does indeed work as far as I can tell for a non-circular list. Here is some Java code that do...
by jaap
Tue Jun 02, 2015 3:19 pm UTC
Forum: Mathematics
Topic: Combinations algorithm and property
Replies: 19
Views: 2580

Re: Combinations algorithm and property

In other words - A set with n elements has nCk subsets of k elements. Find a way to put these subsets in a (circular) list such that each adjacent pair of subsets in the list have k-1 elements in common. Preferably find an algorithm that allows you to generate such a list. This feels a bit like a Gr...
by jaap
Tue Jun 02, 2015 11:52 am UTC
Forum: Coding
Topic: Project Euler
Replies: 411
Views: 141537

Re: Project Euler

This can overflow in that multiplication in cases where your version would not, but if you are worried about that you can use the gcf function to cast out common factors between i and c, and between i and (n+1-i) before multiplying, just like in your Fraction.times function. This is a great point. ...
by jaap
Tue Jun 02, 2015 8:07 am UTC
Forum: Coding
Topic: Project Euler
Replies: 411
Views: 141537

Re: Project Euler

Anyone see any holes in it? :) Not really. There are a few minor stylistic issues: a = 0-a; might as well be a = -a; , and I'd prefer that kind of statement to numerator *= -1; but those are just quibbles. You could also use a=Math.Abs(a); instead of if (a < 0) { a = 0-a; } . There really is no nee...
by jaap
Tue Jun 02, 2015 5:38 am UTC
Forum: Logic Puzzles
Topic: What number pen ??
Replies: 9
Views: 2867

Re: What number pen ??

Vytron wrote:
Spoiler:
Qaanol wrote:And why on earth is pen 4 still empty? I though we agreed to put the RIVER OTTER in there, but it looks like someone put it in pen 6


Okay, I'm puzzled by this, why is RIVER OTTER in 6 and not 4? I thought it was in 4.


Spoiler:
How else does the ARCTIC FOX get to be in pen number 211?
by jaap
Mon May 25, 2015 9:25 pm UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 430609

Re: Favorite math jokes

I used to have a teacher in primary school that gave NP's for good work (nearly perfect) because nothing was ever perfect. Is there a joke here? I believe the joke would be that the teacher put "NP" when the student got all the correct answers, whereas in such a circumstance a...
by jaap
Fri May 22, 2015 12:57 pm UTC
Forum: Science
Topic: Bladeless Wind Turbine: Do joints look better than fans?
Replies: 17
Views: 2842

Re: Bladeless Wind Turbine: Do joints look better than fans?

Question: can it still be used during storms or heavy gusts? If so: big win for the windpole. Wind turbines have to stop during bad weather to prevent them from taking damage. I am not an engineer, but I'd have to say/guess yes, simply because there are no moving parts. There is nothing to turn off...
by jaap
Wed May 20, 2015 3:11 pm UTC
Forum: Logic Puzzles
Topic: Tricky geometric proof
Replies: 8
Views: 5110

Re: Tricky geometric proof

SPACKlick wrote:Your given has some display issues, could you reframe it in words?

Sandor's picture has all the info in. I couldn't see some of the characters in the OP either, but it was fairly easy to deduce they must have been the symbol for perpendicular, but that has now all been captured in Sandor's picture.
by jaap
Mon May 11, 2015 12:24 pm UTC
Forum: Science
Topic: reducing joules to elementary units
Replies: 5
Views: 1196

Re: reducing joules to elementary units

kinetic energy is 1/2 mass * velocity^2, or 1/2 kilograms * meters^2/seconds^2 wolfram alpha agrees: http://www.wolframalpha.com/input/?i=kg+m%5E2+%2F+s%5E2+in+joules except... where did the 1/2 term go? what happened to the coefficient? You are mixing up units and measurements expressed in those u...
by jaap
Sat May 02, 2015 7:56 pm UTC
Forum: Mathematics
Topic: Equations Like f(2x)=4f(x)
Replies: 8
Views: 3523

Re: Equations Like f(2x)=4f(x)

1. f'(x) = f(f(x)) These are called idempotent functions, and they're pretty important in linear algebra. Let y be a point in the range of f. Then there is an x in the domain such that f(x)=y. Then the idempotent condition means that y = f(y). Since y was an arbitrary member of the range, it follow...
by jaap
Mon Apr 27, 2015 5:30 pm UTC
Forum: Logic Puzzles
Topic: Can you solve this?
Replies: 3
Views: 3922

Re: Can you solve this?

It is pretty easy to solve using one of those online substitution cipher tools that gives you the letter frequencies and performs the substitutions you choose. The only tricky bit is the figuring out what the letter c should be, as that is not a normal word. darkness, entropy, time, transposition: t...
by jaap
Sun Apr 26, 2015 10:37 am UTC
Forum: Mathematics
Topic: Tetrahedron with equal heights.
Replies: 1
Views: 1020

Re: Tetrahedron with equal heights.

No. As the tetrahedron has a well-defined single volume, and its volume equals a third the height times the base, it follows that all four faces have the same area. One easy way to ensure all faces have the same area is to use four faces of the same shape. You can for example use the tetrahedron wit...
by jaap
Fri Apr 24, 2015 11:06 am UTC
Forum: Mathematics
Topic: Real roots of polynomials with integer coefficients
Replies: 10
Views: 1896

Re: Real roots of polynomials with integer coefficients

Is there a way to tell whether a polynomial has a multiple root without actually extracting the roots? Yes. If p(x) is the polynomial, then take its derivative p'(x), and then calculate gcd(p(x),p'(x)). If p has a multiple root, then that root will be shared with its derivative, and so this gcd wil...
by jaap
Thu Apr 23, 2015 3:40 pm UTC
Forum: Science
Topic: On friction
Replies: 17
Views: 2950

Re: On friction

You have the mass. That's all you need to find the force of gravity. Once you have that you can find the normal force. Once you have that you can find the force of friction. Once you have that you can calculate acceleration (or deceleration). Once you have that, everything else is easy! Nope, I hav...
by jaap
Tue Apr 21, 2015 8:45 am UTC
Forum: Mathematics
Topic: how to maximize number of beard states?
Replies: 8
Views: 2015

Re: how to maximize number of beard states?

The facial hair styles form a partial order . If style A shaved down into style B, you can say that A>B. There are pairs of styles that are not comparable, i.e. neither can be turned into the other because they both have some hair that the other doesn't. You can draw a graph, like the ones shown on ...
by jaap
Sat Apr 18, 2015 8:16 am UTC
Forum: Logic Puzzles
Topic: forget Cheryl's Birthday
Replies: 1
Views: 1713

Re: forget Cheryl's Birthday

We've had versions of this puzzle lots of times before: http://forums.xkcd.com/viewtopic.php?f=3&t=131 http://forums.xkcd.com/viewtopic.php?f=3&t=9308 http://forums.xkcd.com/viewtopic.php?f=3&t=45733 http://forums.xkcd.com/viewtopic.php?f=3&t=65980 http://forums.xkcd.com/viewtopic.ph...
by jaap
Wed Apr 15, 2015 3:29 pm UTC
Forum: Science
Topic: Earth's trajectory if the sun disappeared...?
Replies: 48
Views: 7255

Re: Earth's trajectory if the sun disappeared...?

I once did that same calculation for the moon (i.e. take twice the gravitational force it exerts to get the difference between when it's overhead and when it is opposite). This was in order to show that it would have virtually no effect on the blood circulation of a human being. It indeed wouldn't (...
by jaap
Wed Apr 15, 2015 9:48 am UTC
Forum: Logic Puzzles
Topic: Cheryl's Birthday
Replies: 29
Views: 5371

Re: Cheryl's Birthday

A slight tangent to the original question, but I know that the problem is asking what Cheryl's birthday is based on you being an outside observer to the problem. I was wondering if there's a way to work out how Albert was able to know the date based on him knowing that Bernard now knows the date. A...
by jaap
Thu Apr 02, 2015 7:37 am UTC
Forum: Logic Puzzles
Topic: Demonstrating objects are of equal weight
Replies: 12
Views: 4388

Re: Demonstrating objects are of equal weight

Zero. The problem can be solved without using a balance scale at all. 1. Weigh all the objects on a digital scale of sufficient precision and accuracy. 2. Weigh a single object on the same digital scale. 3. Divide the results. If the quotient equals the number of objects—meaning in particular it is...
by jaap
Tue Mar 31, 2015 5:04 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 378
Views: 101060

Re: Math: Fleeting Thoughts

Someone recently showed me a number (which I don't recall off the top of my head) which when multiplied by 2 or multiplied by 3 resulted in all the same digits, just rearranged. Is there a name for numbers with that property? Is there anything fancy being done 'under the hood' that makes numbers li...
by jaap
Tue Mar 24, 2015 12:34 pm UTC
Forum: Fictional Science
Topic: Super-Powers (Super-Speed!)
Replies: 73
Views: 13307

Re: Super-Powers (Super-Speed!)

Wait, is this true? If she's slowing time down, that means wavelengths will get longer; visible light would 'lengthen' into UV, and shorter wavelengths (like IR) would 'lengthen' into the visible spectrum. Unless I'm misunderstanding something? Infrared has a longer wavelength (lower frequency) tha...
by jaap
Thu Mar 19, 2015 10:28 am UTC
Forum: Mathematics
Topic: Probability of K sequence of X heads out of N coin flips
Replies: 6
Views: 1663

Re: Probability of K sequence of X heads out of N coin flips

This is typically a problem where the Inclusion-Exclusion Principle comes into play. To be honest however, I would not even attempt to do this in this manner, because there is a complication that hasn't been pointed out yet. The K sequences of X heads and their tail separators don't always take up t...
by jaap
Fri Mar 13, 2015 7:12 pm UTC
Forum: Logic Puzzles
Topic: Ah! Help! How do you solve this? (Nim Variation I think)
Replies: 7
Views: 2167

Re: Ah! Help! How do you solve this? (Nim Variation I think)

If both Alice and Bob are playing optimally, what can you say about the relationship between the burnt piece and every cut performed? There is no reason to perform a cut that doesn't touch the side of the burnt piece. It would just leave more edible parts for the opponent. The burnt piece only ...
by jaap
Fri Mar 13, 2015 6:55 pm UTC
Forum: Logic Puzzles
Topic: Ah! Help! How do you solve this? (Nim Variation I think)
Replies: 7
Views: 2167

Re: Ah! Help! How do you solve this? (Nim Variation I think)

Hints: Consider only the squares that lie in the same row or in the same column as the burnt square, and ignore all other squares. Those squares as described in my previous hint form four lines radiating out from the burnt square. What does a move do to these four lines of squares? How many lines ca...
by jaap
Sun Mar 08, 2015 4:29 pm UTC
Forum: Mathematics
Topic: Dice probabilities and King of Tokyo
Replies: 5
Views: 2131

Re: Dice probabilities and King of Tokyo

I didn't do any actual math, but my simulations show the answer to be a hair short of 14%. I was updating my previous post when you posted this. I just did a quick Monte Carlo simulation, and get answers much closer to the 19.7% that I calculated: 196565/1000000=0.196565 196636/1000000=0.196636 196...
by jaap
Sun Mar 08, 2015 2:16 pm UTC
Forum: Mathematics
Topic: Dice probabilities and King of Tokyo
Replies: 5
Views: 2131

Re: Dice probabilities and King of Tokyo

We realised that it's a 1 in 720 chance of rolling this result on the first roll No, it isn't. There are 6!=720 ways to make 6 different numbers out of the 6^6=46656 possible combinations of any 6 numbers. This is a probability of 720/46656 or about 1 in 65. With the re-rolls it is much more compli...
by jaap
Thu Mar 05, 2015 10:33 am UTC
Forum: Language/Linguistics
Topic: Misdeciphering unfamiliar words
Replies: 8
Views: 4141

Re: Misdeciphering unfamiliar words

But the misanalysis of misled imposes a different pronunciation – /ˈmɪzl̩d/ – whereas vernier is pronounced the same in either analysis. Is it? I pronounce 'vernier' as two syllables, but if I were to mis-analyze it as a comparative of *verny, I would pronounce it as three. But perhaps I'm incorrec...
by jaap
Wed Mar 04, 2015 5:34 pm UTC
Forum: Language/Linguistics
Topic: Misdeciphering unfamiliar words
Replies: 8
Views: 4141

Re: Misdeciphering unfamiliar words

Lazar wrote:
Envelope Generator wrote:Does this kind of mistake have a name?

Yes, it's a mondegreen.

I'm not so sure, as a Mondegreen is based on mishearing a word or phrase, so the erroneous word will sound very similar. This is about misreading it, like "misled".
by jaap
Sat Feb 21, 2015 7:13 am UTC
Forum: Science
Topic: [ASTRONOMY?] [MATHEMATICS?] [SF?] Trying to make log scale
Replies: 3
Views: 1480

Re: [ASTRONOMY?] [MATHEMATICS?] [SF?] Trying to make log sca

At this moment the factor between subsequent classes is 16. To split that factor into k subdivisions, you need to use the k-th root of it as the factor between those subdivisions. So if a class has the range M to 16*M, the subdivisions have the ranges M to M * 16 1/16 , M * 16 1/16 to M * 16 2/16 M ...
by jaap
Fri Feb 20, 2015 9:41 pm UTC
Forum: Mathematics
Topic: Permutation 'logarithm'
Replies: 4
Views: 1787

Re: Permutation 'logarithm'

Isn't this the discrete logarithm ? Yes, but: This is indeed the discrete logarithm, but in the context of a permutation group. I took this to mean that the elements p and k are expressed as permutations of some set of a reasonable size. Of course, every finite group G is a permutation group acting...
by jaap
Fri Feb 20, 2015 2:44 pm UTC
Forum: Mathematics
Topic: Permutation 'logarithm'
Replies: 4
Views: 1787

Re: Permutation 'logarithm'

I'm sure this can't be a new topic seeing how old group theory is, but my Google-fu has failed to turn up any relevant articles. Suppose you have permutations p and k , and you know that k = p n for some n, how do you find n without manually applying p n times? It is not really that different from ...
by jaap
Sun Feb 15, 2015 6:00 pm UTC
Forum: Mathematics
Topic: number of K digit numbers divisible by prime
Replies: 9
Views: 2156

Re: number of K digit numbers divisible by prime

What is the apporach if p is small?. Would like to hear it To quote the Project Euler FAQ: I learned so much solving problem XXX so is it okay to publish my solution elsewhere? It appears that you have answered your own question. There is nothing quite like that "Aha!" moment when you fin...
by jaap
Sun Feb 15, 2015 2:42 pm UTC
Forum: Mathematics
Topic: number of K digit numbers divisible by prime
Replies: 9
Views: 2156

Re: number of K digit numbers divisible by prime

I agree that this dynamic programming approach is the way to go. There is however a certain Project Euler problem about this in which k is very large relative to N, and then you need several more tricks to calculate the result. If p is also small compared to k, I think I might have an approach. It ...
by jaap
Fri Feb 13, 2015 2:23 pm UTC
Forum: Mathematics
Topic: number of K digit numbers divisible by prime
Replies: 9
Views: 2156

Re: number of K digit numbers divisible by prime

To move from one level to the next, notice that if an (i-1) digit number gives a remainder of r when divided by p and has a digit sum of s has a d appended to the front, then its remainder is r + d*10^i (mod p) and digit sum of s+d. You can do a little better [...snip...] It think it is easier to a...

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