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.

- Thu Mar 03, 2016 8:51 am UTC
- Forum: Logic Puzzles
- Topic: Optimize tiling for a 50x50 grid
- Replies:
**7** - Views:
**2838**

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.

- Mon Feb 29, 2016 4:09 pm UTC
- Forum: Mathematics
- Topic: Math: Fleeting Thoughts
- Replies:
**378** - Views:
**100893**

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 ...

- Fri Feb 26, 2016 12:10 am UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9738** - Views:
**1549518**

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...

- Tue Feb 23, 2016 2:28 pm UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9738** - Views:
**1549518**

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...

- Mon Feb 22, 2016 1:39 am UTC
- Forum: Logic Puzzles
- Topic: Two gold nugget puzzle
- Replies:
**17** - Views:
**3885**

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...

- Sat Feb 20, 2016 1:04 pm UTC
- Forum: Logic Puzzles
- Topic: Another smullyanesque puzzle
- Replies:
**14** - Views:
**3647**

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 ...

- Fri Feb 19, 2016 12:12 am UTC
- Forum: Logic Puzzles
- Topic: Simple maths problem?
- Replies:
**9** - Views:
**2460**

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+...

- Thu Feb 18, 2016 8:18 pm UTC
- Forum: Logic Puzzles
- Topic: Simple maths problem?
- Replies:
**9** - Views:
**2460**

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

Edited to add extra pair of brackets.

Edited to add extra pair of brackets.

- Thu Feb 18, 2016 8:07 pm UTC
- Forum: Logic Puzzles
- Topic: Simple maths problem?
- Replies:
**9** - Views:
**2460**

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

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

- Mon Feb 15, 2016 5:39 pm UTC
- Forum: Mathematics
- Topic: Combinatorics : Castle, rooms and doors
- Replies:
**14** - Views:
**2547**

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 ...

- Sun Feb 14, 2016 11:15 am UTC
- Forum: Mathematics
- Topic: Combinatorics : Castle, rooms and doors
- Replies:
**14** - Views:
**2547**

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...

- Fri Feb 12, 2016 4:05 pm UTC
- Forum: Mathematics
- Topic: Cardinality of subset of the powerset of naturals
- Replies:
**5** - Views:
**1403**

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 ...

- Tue Feb 09, 2016 1:16 pm UTC
- Forum: Logic Puzzles
- Topic: A question about stacking spheres
- Replies:
**2** - Views:
**1892**

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...

- Tue Feb 09, 2016 10:36 am UTC
- Forum: Logic Puzzles
- Topic: A question about stacking spheres
- Replies:
**2** - Views:
**1892**

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...

- Mon Feb 08, 2016 4:15 pm UTC
- Forum: Mathematics
- Topic: Coin flip problem
- Replies:
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**1378**

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...

- Mon Feb 08, 2016 9:25 am UTC
- Forum: Mathematics
- Topic: Coin flip problem
- Replies:
**6** - Views:
**1378**

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...

- Thu Feb 04, 2016 1:21 am UTC
- Forum: Movies and TV Shows
- Topic: Star Wars: Episode 7: Electric Boogaleven
- Replies:
**479** - Views:
**98601**

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...

- Fri Jan 15, 2016 5:48 pm UTC
- Forum: Logic Puzzles
- Topic: A question about stacking dominoes
- Replies:
**5** - Views:
**1858**

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...

- Fri Jan 15, 2016 5:35 pm UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
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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.

Edit:

Colin Wright pointed out that this is an extreme case of the infinite family in the paper:

Edit:

Colin Wright pointed out that this is an extreme case of the infinite family in the paper:

- Fri Jan 15, 2016 3:49 pm UTC
- Forum: Logic Puzzles
- Topic: A question about stacking dominoes
- Replies:
**5** - Views:
**1858**

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: ⋅...

- Thu Jan 14, 2016 7:06 am UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
**16921**

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 ...

- Wed Jan 13, 2016 6:40 pm UTC
- Forum: Logic Puzzles
- Topic: Unusual Cake Slicing
- Replies:
**84** - Views:
**16921**

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...

- Tue Jan 05, 2016 9:03 am UTC
- Forum: Movies and TV Shows
- Topic: Star Wars: Episode 7: Electric Boogaleven
- Replies:
**479** - Views:
**98601**

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,...

- Tue Jan 05, 2016 8:53 am UTC
- Forum: Logic Puzzles
- Topic: Blue Eyes with Superrationality
- Replies:
**48** - Views:
**8822**

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 ...

- Thu Dec 31, 2015 6:50 am UTC
- Forum: Logic Puzzles
- Topic: Probability of ending up in room N
- Replies:
**3** - Views:
**1886**

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...

- Wed Dec 30, 2015 10:27 am UTC
- Forum: Logic Puzzles
- Topic: Probability of ending up in room N
- Replies:
**3** - Views:
**1886**

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...

- Tue Dec 29, 2015 12:14 am UTC
- Forum: Logic Puzzles
- Topic: Escape the bear in the circle?
- Replies:
**22** - Views:
**4536**

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...

- Sun Dec 27, 2015 9:02 am UTC
- Forum: Logic Puzzles
- Topic: Escape the bear in the circle?
- Replies:
**22** - Views:
**4536**

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 ...

- Mon Nov 30, 2015 12:26 pm UTC
- Forum: Movies and TV Shows
- Topic: Doctor Whom
- Replies:
**4894** - Views:
**558422**

- Tue Nov 24, 2015 2:35 pm UTC
- Forum: Coding
- Topic: [Answered] Basic question about storing function results
- Replies:
**3** - Views:
**2802**

- Tue Nov 24, 2015 11:47 am UTC
- Forum: Mathematics
- Topic: Least numbers discarded when dealing cards
- Replies:
**30** - Views:
**5167**

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...

- Fri Nov 20, 2015 10:54 am UTC
- Forum: Mathematics
- Topic: Least numbers discarded when dealing cards
- Replies:
**30** - Views:
**5167**

Am I missing something or are people way overthinking this? Just put the numbers 1 through 52 in an array and shuffle it. Dealing cards is as simple as pulling out elements starting from the first index and working your way down. The problem is that in step 2 of that shuffling algorithm you need to...

- Wed Nov 18, 2015 3:44 pm UTC
- Forum: Logic Puzzles
- Topic: Find the Mole
- Replies:
**5** - Views:
**1947**

This is a repeat of:

viewtopic.php?f=3&t=62767

viewtopic.php?f=3&t=62767

- Mon Nov 16, 2015 9:33 pm UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9738** - Views:
**1549518**

This discussion of for reminds me of this beautiful yet ghastly construct:

Code: Select all

`for(unsigned i = 10; i --> 0;)`

{

//stuff

}

- Thu Nov 12, 2015 9:31 am UTC
- Forum: Computer Science
- Topic: Reconstructing a tiling from "is-adjacent-to" data?
- Replies:
**10** - Views:
**6511**

By the way, the solution is usually not unique. For example, if you have 4 countries where each is adjacent to all three others, then you can draw a map in 8 distinct ways: You can choose any of the 4 countries to be in the middle, landlocked by the other three countries, and those other three can b...

- Wed Nov 11, 2015 11:16 am UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**146** - Views:
**28689**

There is a loophole in the puzzle wording: A perfectly flat plane does not necessarily have to be perfectly level. If it's a sloping flat plane, you will automatically reach the outside of the circle. I also thought about what it means to have a perfectly flat surface on a round earth. Unfortuna...

- Tue Nov 10, 2015 6:23 pm UTC
- Forum: Computer Science
- Topic: Reconstructing a tiling from "is-adjacent-to" data?
- Replies:
**10** - Views:
**6511**

You can think of this data as a graph, where the countries are vertices and the 'is adjacent to' relation gives you the edges. Your question then boils down to this: Given a planar graph, draw it without any crossing edges. Or in more mathematical terms, find an embedding of a planar graph in the pl...

- Mon Nov 09, 2015 4:21 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**146** - Views:
**28689**

I wasn't clear there, I meant it wouldn't work for this puzzle's situation, not for a ball situation. If the floor can't distort here and the normal forces are all purely vertical, I don't see how the CoM of the system (gold block + person) can be shifted laterally. Sorry, for misunderstanding you....

- Mon Nov 09, 2015 3:08 pm UTC
- Forum: Logic Puzzles
- Topic: Escape the Frictionless Circle
- Replies:
**146** - Views:
**28689**

The first thing that comes to mind is the answer to a problem that I read at some point: If a ball is rolling on an infinite, perfectly flat, surface, in a vacuum, will it ever stop? The answer was yes, because the ball exerts more force on the surface in the direction it is traveling in than the o...

- Fri Nov 06, 2015 5:28 pm UTC
- Forum: Logic Puzzles
- Topic: Timed Bridge Problem
- Replies:
**3** - Views:
**1737**