Search found 2067 matches

by jaap
Sat May 07, 2016 7:55 am UTC
Forum: Logic Puzzles
Topic: What is the last number (alphabetically)?
Replies: 12
Views: 4544

Re: What is the last number (alphabetically)?

Spoiler:
zero
by jaap
Sat Apr 16, 2016 10:21 am UTC
Forum: Computer Science
Topic: Reverse engineering cyclical function from observed outputs
Replies: 4
Views: 4472

Re: Reverse engineering cyclical function from observed outputs

Yes, 40-90, thanks. Any ideas on how to get those scalars right? Trial and error is proving tedious... these could be arbitrary rational numbers chosen by an RNG. I guess that means any value I guessed could be off by an arbitrary amount, which would put the rounding errors in an arbitrary place on...
by jaap
Fri Apr 15, 2016 7:57 am UTC
Forum: Computer Science
Topic: Reverse engineering cyclical function from observed outputs
Replies: 4
Views: 4472

Re: Reverse engineering cyclical function from observed outputs

The values seem to range from 40 to 90, not 50 to 90. It looks to me like it increases by 21 or 22 as x increases, except that if that brings its value over 90 then 51 is subtracted to bring it back into the [40,90] range. Similarly in the y direction, it increases by 26 or 27 each time. So it is pr...
by jaap
Fri Mar 11, 2016 3:43 pm UTC
Forum: Mathematics
Topic: Pi root of -1
Replies: 8
Views: 2495

Re: Pi root of -1

(-1) 2 = 1 This means that (-1) x can only ever evaluate to three results: 1, -1, or +-i. No it does not mean that. For example, consider the complex number (1+i)/sqrt(2). If you square this, you get: [(1+i)/sqrt(2)] 2 = (1+i) 2 /2 = (1*1 + 1*i + i*1 + i*i)/2 = (1 + 2i + -1)/2 = i So this number to...
by jaap
Fri Mar 11, 2016 1:10 am UTC
Forum: Mathematics
Topic: finite field question
Replies: 1
Views: 1742

Re: finite field question

You seem to be assuming that log in this context is a function from GF(2 n ) to GF(2 n ), but it is not. The multiplicative group of GF(2 n ) is cyclic of order 2 n -1. If g is a generator of that group, then you are multiplying two elements a=g e and b=g f as a*b = g e g f = g e+f = c. The addition...
by jaap
Thu Mar 10, 2016 12:51 pm UTC
Forum: Language/Linguistics
Topic: Regional Dialect and Idiolect Oddities (pronunciation)
Replies: 941
Views: 225349

Re: Regional Dialect and Idiolect Oddities (pronunciation)

Eebster the Great wrote:
Derek wrote:"At the weekend"? Seriously? It's not a fucking location!

Neither is "at the right moment."

Also "At nine o'clock", "At noon", or if you want an example with a period of time rather than an instant, there is "At night".
by jaap
Mon Mar 07, 2016 2:09 pm UTC
Forum: Mathematics
Topic: Finite sequence, infinite average?
Replies: 5
Views: 1655

Re: Finite sequence, infinite average?

See also almost surely. There are almost surely going to be only a finite number of coin tosses. Whilst going on forever is a possible outcome, the probability of that is nevertheless exactly zero, and the probability of finite tosses is exactly 1.
by jaap
Fri Mar 04, 2016 9:45 am UTC
Forum: Logic Puzzles
Topic: Optimize tiling for a 50x50 grid
Replies: 7
Views: 3245

Re: Optimize tiling for a 50x50 grid

Impressive Jaap! I only managed to get one with 17 squares left with graph paper. I didn't think it was possible to fill all 2500. If you ran a computer algorithm, do you mind sharing the code? It's my PolyForm Puzzle Solver Java applet on my puzzle site. If you can't get it to run in your browser,...
by jaap
Fri Mar 04, 2016 6:36 am UTC
Forum: Logic Puzzles
Topic: Optimize tiling for a 50x50 grid
Replies: 7
Views: 3245

Re: Optimize tiling for a 50x50 grid

Here's a solution using six 5x5 tiles and all of the others. Only 17 squares are left empty.
Spoiler:
puzzle.png


Edit:
Here's one that fills it completely. Nine 5x5's are used.
Spoiler:
puzzle2.png
by jaap
Thu Mar 03, 2016 8:51 am UTC
Forum: Logic Puzzles
Topic: Optimize tiling for a 50x50 grid
Replies: 7
Views: 3245

Re: Optimize tiling for a 50x50 grid

Cradarc wrote:3. A M x N tile placed on the grid will give you P = NM - 0.5*(N+M) points (ie. area - semiperimeter)

That's not the semiperimeter, it's a quarter of the perimeter.
by jaap
Mon Feb 29, 2016 4:09 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 382
Views: 116302

Re: Math: Fleeting Thoughts

You would need at least one bit then to indicate whether the gap was to be represented by one or two bytes (or really 7 or 15 bits). But anyway, it's kind of a useless list, because to use the list to tell if a given number is prime, you would have to start from the beginning and keep adding until ...
by jaap
Fri Feb 26, 2016 12:10 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9848
Views: 1732566

Re: Coding: Fleeting Thoughts

Why not just read 3 bytes for every random number? Then you have an even range to run the modulus on and all is right in the world again. 2^24 is not divisible by 3 so either you have a non-uniform distribution, or you will have to discard one of those 2^24 cases and accept that there is a 1 in 2^2...
by jaap
Tue Feb 23, 2016 2:28 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9848
Views: 1732566

Re: Coding: Fleeting Thoughts

There have been some threads about generating one or more uniform random numbers in one range when given a random number generator with a different range, e.g. a 6-sided die using only coin flips. Here is the most recent one in Mathematics: http://forums.xkcd.com/viewtopic.php?f=17&t=113023 Here...
by jaap
Mon Feb 22, 2016 1:39 am UTC
Forum: Logic Puzzles
Topic: Two gold nugget puzzle
Replies: 17
Views: 4664

Re: Two gold nugget puzzle

I can do it in 12. If you split it into 4 piles, it is possible to eliminate the lightest two piles using four weighings. Label the piles A, B, C, D, then weigh A vs B, and C vs D. Let's assume that B and D were the lighter ones (which we can do without loss of generality - swap labels if th...
by jaap
Sat Feb 20, 2016 1:04 pm UTC
Forum: Logic Puzzles
Topic: Another smullyanesque puzzle
Replies: 14
Views: 4057

Re: Another smullyanesque puzzle

You meet two married couples on the island of knights and knaves. (Knights always tell the truth, knaves always tell lies.) They make the following statements: Adam: My spouse is a knave. Betty: Adam is a knight. Cecilia: Me and my spouse are the same. David: Me and Cecilia are the same. 1) Who is ...
by jaap
Fri Feb 19, 2016 12:12 am UTC
Forum: Logic Puzzles
Topic: Simple maths problem?
Replies: 9
Views: 2741

Re: Simple maths problem?

Do you know if it's possible to get every answer from 1 to 100 using these numbers and any combination of operators? Just curious. Sure, that is still quite easy: 1 1+2+3+4-5+6+7-8-9 2 1*2+3-4+5+6+7-8-9 3 1+2+3-4+5+6+7-8-9 4 1*2-3+4+5+6+7-8-9 5 1+2-3+4+5+6+7-8-9 6 1*2-3+4+5+6-7+8-9 7 1+2-3+4+5+6-7+...
by jaap
Thu Feb 18, 2016 8:18 pm UTC
Forum: Logic Puzzles
Topic: Simple maths problem?
Replies: 9
Views: 2741

Re: Simple maths problem?

((1+2)/3)^4 * 5 +6 +7 -8 -9


Edited to add extra pair of brackets.
by jaap
Thu Feb 18, 2016 8:07 pm UTC
Forum: Logic Puzzles
Topic: Simple maths problem?
Replies: 9
Views: 2741

Re: Simple maths problem?

Isn't that rather easy?
1+2+3+4-5+6+7-8-9
1-2-3+4+5+6+7-8-9
1+2+3+4+5-6-7+8-9
1+2-3-4+5-6+7+8-9
by jaap
Mon Feb 15, 2016 5:39 pm UTC
Forum: Mathematics
Topic: Combinatorics : Castle, rooms and doors
Replies: 14
Views: 2783

Re: Combinatorics : Castle, rooms and doors

If we find a general formula for nxn with 0,1,2,3,4 doors then we wil obtain 2 doors by substraction. Subtraction from what? The number of nxn configurations where all the rooms have the same number of doors? How will that be calculated? Anyway, here are the results that I got by computer: x 1 2 3 ...
by jaap
Sun Feb 14, 2016 11:15 am UTC
Forum: Mathematics
Topic: Combinatorics : Castle, rooms and doors
Replies: 14
Views: 2783

Re: Combinatorics : Castle, rooms and doors

I get 86 for 2x2. Starting from 54 for the 3-room"L", 11 have two open doors towards the fourth room (->11 options), 11 have no open door (->11 options), and 32 have one open door (->2*32 options), for a total of 86 options. Finding that number of 11 was not trivial, so I don't see an eas...
by jaap
Fri Feb 12, 2016 4:05 pm UTC
Forum: Mathematics
Topic: Cardinality of subset of the powerset of naturals
Replies: 5
Views: 1595

Re: Cardinality of subset of the powerset of naturals

But for c = 0, isn't there still no natural number k which describes the size of infinite elements of S? Yet, since there is only one set in S of size |k| for each k in N (because k^c = 1), S is now countable. To restate what arbiteroftruth is getting at: Your statement "for all k in N, there ...
by jaap
Tue Feb 09, 2016 1:16 pm UTC
Forum: Logic Puzzles
Topic: A question about stacking spheres
Replies: 2
Views: 1998

Re: A question about stacking spheres

I assume you can't just remove spheres again? Yes, that is what I meant but didn't actually specify. Let's see the bottom layer can only have a even number sticking up, and the 3x3 layer only an uneven number and if an uneven number is alredy occupied on the 2x2 layer then everything is fine. B...
by jaap
Tue Feb 09, 2016 10:36 am UTC
Forum: Logic Puzzles
Topic: A question about stacking spheres
Replies: 2
Views: 1998

A question about stacking spheres

From the same person who asked me a question about stacking dominoes , here is a question about stacking spheres. Suppose you want to build a square pyramid made up of 30 spheres. So the bottom layer is a 4x4 arrangement of touching spheres, and it has 3x3, 2x2 and 1x1 layers on top. The building bl...
by jaap
Mon Feb 08, 2016 4:15 pm UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1555

Re: Coin flip problem

With that you should be able to follow the rest of Cauchy's post that transforms that second term, the probability of a sequence that reaches m but ends below it, into the probability of a sequence that ends above m. I appreciate that you assumed I was the one explaining, but it just ain't so. Cred...
by jaap
Mon Feb 08, 2016 9:25 am UTC
Forum: Mathematics
Topic: Coin flip problem
Replies: 6
Views: 1555

Re: Coin flip problem

This is a trick I learned once for the "drunkard's walk" formulation. Let X k equal the number of heads minus the number of tails after k tosses. The probability that X k stays below m forever is equal to P(X n < m) - P(X n < m and X k = m for some k). For each sequence of flips in the la...
by jaap
Thu Feb 04, 2016 1:21 am UTC
Forum: Movies and TV Shows
Topic: Star Wars: Episode 7: Electric Boogaleven
Replies: 479
Views: 107770

Re: Star Wars: Episode 7: Electric Boogaleven

Well Cloverfield clearly hasn't vanished down the memory hole yet if you're mentioning it... People know it existed, sure. But nobody cares about it. Nobody thinks back and says "man, you know what was a good movie?" In twenty years, people won't even remember it was a thing unless they s...
by jaap
Fri Jan 15, 2016 5:48 pm UTC
Forum: Logic Puzzles
Topic: A question about stacking dominoes
Replies: 5
Views: 1997

Re: A question about stacking dominoes

So you need atleast 2x dominoes to support x dominoes. Anyway let's start building in the reverse direction, if you can add a valid layer below a layer you could have done it the other way around. I assume that adding dominoes to the layer below that don't support any stone does not improve...
by jaap
Fri Jan 15, 2016 5:35 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 18513

Re: Unusual Cake Slicing

Here is a dissection I found that I believe to be new, which is completely unrelated to any of the ones in this thread or in the paper.
circledissection.gif
circledissection.gif (1.77 KiB) Viewed 1432 times


Edit:
Colin Wright pointed out that this is an extreme case of the infinite family in the paper:
circledissection2.png
by jaap
Fri Jan 15, 2016 3:49 pm UTC
Forum: Logic Puzzles
Topic: A question about stacking dominoes
Replies: 5
Views: 1997

A question about stacking dominoes

Here's a neat question someone asked me when he was developing a two-player game. Suppose you have a large number of identical 2x1 tiles, i.e. dominoes, and a large board with a square grid of the same size as the dominoes. You can place the dominoes on the board, but must follow these rules: ⋅...
by jaap
Thu Jan 14, 2016 7:06 am UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 18513

Re: Unusual Cake Slicing

One year later, gizmodo catches up. http://gizmodo.com/mathematicians-have-found-crazy-new-ways-to-cut-pizza-i-1751776752 The paper was put on arxiv a month ago. It is doing the rounds now because New Scientist published an article about it last week. While the paper is from last year, I would not ...
by jaap
Wed Jan 13, 2016 6:40 pm UTC
Forum: Logic Puzzles
Topic: Unusual Cake Slicing
Replies: 84
Views: 18513

Re: Unusual Cake Slicing

There has been a new development: http://arxiv.org/pdf/1512.03794.pdf This paper shows some interesting new dissections of the circle into equal parts, not all on the boundary. It even references this thread. Still no solutions where the centre falls inside a piece, though. See also: http://www.ifls...
by jaap
Tue Jan 05, 2016 9:03 am UTC
Forum: Movies and TV Shows
Topic: Star Wars: Episode 7: Electric Boogaleven
Replies: 479
Views: 107770

Re: Star Wars: Episode 7: Electric Boogaleven

There's something in this movie's final fight that I'm sure I have seen before in some other film, but I can't think which one, namely the way Kylo Ren thumps his wounded side, as if to keep his body working Does anyone know where this was done before? Edit: I think it could be from a samurai movie,...
by jaap
Tue Jan 05, 2016 8:53 am UTC
Forum: Logic Puzzles
Topic: Blue Eyes with Superrationality
Replies: 48
Views: 9760

Re: Blue Eyes with Superrationality

Even though they all can agree that there is at least one blue-eyed person on the island, they don't mean the same thing when they say that. It really means, "amongst the N-1 people that are not me, there is at least one blue-eyed person". That statement is self-referential, and refers to ...
by jaap
Thu Dec 31, 2015 6:50 am UTC
Forum: Logic Puzzles
Topic: Probability of ending up in room N
Replies: 3
Views: 2066

Re: Probability of ending up in room N

Not really. You also have an infinite number of rounds to play, and each round has a non-zero chance of success. While it is theoretically possible to lose an infinite number of times, the probability of that happening is zero. You are almost surely going to win some round. What about this scenario...
by jaap
Wed Dec 30, 2015 10:27 am UTC
Forum: Logic Puzzles
Topic: Probability of ending up in room N
Replies: 3
Views: 2066

Re: Probability of ending up in room N

I've just "dreamt" this up, so if it's unsolvable (or even too easy) .... go easy on me please :) So you check into a plush hotel and pay your $40 for 1 night's stay. You are then told you've been allocated room 1 (which is a bit of a bummer. as the rooms get better as the room number inc...
by jaap
Tue Dec 29, 2015 12:14 am UTC
Forum: Logic Puzzles
Topic: Escape the bear in the circle?
Replies: 22
Views: 5274

Re: Escape the bear in the circle?

This is because your strategy would push the person closer and closer to the boundary. Even while moving in a circle, the bear can position itself to force the tangential direction of the prey's circular path to move towards the boundary. The tangential direction of the person's path, by definition...
by jaap
Sun Dec 27, 2015 9:02 am UTC
Forum: Logic Puzzles
Topic: Escape the bear in the circle?
Replies: 22
Views: 5274

Re: Escape the bear in the circle?

The explanations Notzeb linked to are suspiciously like the Zeno's paradox. At every step, the lion/bear gets closer to the person, yet it never fully overlap the person. Basically, the bear can get arbitrarily close, but never actually reach its prey. I agree that the proof in that paper there is ...
by jaap
Mon Nov 30, 2015 12:26 pm UTC
Forum: Movies and TV Shows
Topic: Doctor Whom
Replies: 4917
Views: 643433

Re: Doctor Whom

by jaap
Tue Nov 24, 2015 11:47 am UTC
Forum: Mathematics
Topic: Least numbers discarded when dealing cards
Replies: 30
Views: 5794

Re: Least numbers discarded when dealing cards

Do you understand what my method does? No, I have no idea what s % n function does. That is the 'mod' operator, and s%n means the remainder when dividing s by n. So 1000%52 = 12 because 1000=19*52+12. Perhaps if I add 52 to 52 until I find a number 100...00 it could be used in base 52. Though I'd s...

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