## Search found 103 matches

- Mon Apr 03, 2017 12:36 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1819: "Sweet 16"
- Replies:
**49** - Views:
**10849**

### Re: 1819: "Sweet 16"

The stilt team could fight for a draw at best. They could never intercept a pass or block a shot because they're too high up, they can't dribble the ball. They'll end up committing numerous technical fouls for kicking their opponents and losing. Or they will succeed in fighting for a draw, then be m...

- Mon Apr 03, 2017 9:50 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1819: "Sweet 16"
- Replies:
**49** - Views:
**10849**

### Re: 1819: "Sweet 16"

I think it will be a close call between team with one dog, the 1988 Lakers and the bad team which would make a good Cinderella story. I guess the NBA2K17 top players shouldn't be underestimated, too. A lot of the top players of the FIFA video game series are actually decent footballers (some even pr...

- Wed Feb 03, 2016 6:43 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1638: "Backslashes"
- Replies:
**62** - Views:
**11602**

### Re: 1638: "Backslashes"

You should try CMake macros. They resolve backslashes every time. So if you have a macro, calling a macro, calling a macro, needing a backslash you need to call: macro("\\\\\\\\") ... then you start writing scripts which generate power-of-two backslashes, based on the call stack depth, unt...

- Mon May 18, 2015 12:20 pm UTC
- Forum: Logic Puzzles
- Topic: White House Puzzle: Alice and Bob guessing coin flips
- Replies:
**3** - Views:
**2411**

- Thu Apr 30, 2015 9:19 am UTC
- Forum: Computer Science
- Topic: A fun problem: Biggest difference between elements
- Replies:
**9** - Views:
**4815**

### A fun problem: Biggest difference between elements

I stumbled upon this problem recently and couldn't solve it on my own. However I know the solution now, and it is a legitimate one (initially I doubted that this would be possible). You have an array of real numbers in some random order. Devise an algorithm that calculates the biggest difference bet...

- Sun Dec 21, 2014 7:33 pm UTC
- Forum: Mathematics
- Topic: A seemingly simple geometry problem
- Replies:
**12** - Views:
**3511**

### Re: A seemingly simple geometry problem

All right, I suspected that might not work. Well, since you know every angle except the unknowns, you can assume the length of AB is 1, and then use Law of Sines to calculate the length of every line segment. Once you know the lengths of CX and DX, you can use the angle CXD to Law Of Sines your way...

- Sun Dec 21, 2014 9:10 am UTC
- Forum: Mathematics
- Topic: A seemingly simple geometry problem
- Replies:
**12** - Views:
**3511**

### Re: A seemingly simple geometry problem

Sadly, none of those work. I don't think there's a solution with simple angle arithmetic over the quadrilateral only.

- Sun Dec 21, 2014 7:28 am UTC
- Forum: Mathematics
- Topic: A seemingly simple geometry problem
- Replies:
**12** - Views:
**3511**

### A seemingly simple geometry problem

We have a quadrilateral ABCD. The angles CAB, ABD, DBC, CAD are a, b, c, d respectively. What is the angle BDC? Now, we can use the laws of sines and cosines to create a system of equations. But it's... well... ugly. Is there an easier way to solve this? Is there a way that doesn't use trigonometry ...

- Mon Sep 29, 2014 2:10 pm UTC
- Forum: Logic Puzzles
- Topic: Independent sort
- Replies:
**15** - Views:
**5376**

### Re: Independent sort

The answer is no, the prisoner is not allowed to pick up a card, and then use the information of what is revealed under that card to decide which of the other two piles to place the card he just picked up. That would be a neat variation though, and may be worth exploring too. I don't think it would...

- Sat Sep 27, 2014 7:00 pm UTC
- Forum: Logic Puzzles
- Topic: Independent sort
- Replies:
**15** - Views:
**5376**

### Independent sort

There's a room with three open boxes (clearly marked "left", "middle", "right") and three cards in the boxes (clearly marked "1", "2", "3"). The position of the cards in the boxes is unknown (could be that all cards are in one of them or an...

- Thu Sep 11, 2014 5:36 pm UTC
- Forum: Logic Puzzles
- Topic: Tournament Scheduling
- Replies:
**6** - Views:
**3068**

### Re: Tournament Scheduling

I don't get the time slots thing. Each game is supposed to be played at a specific time, but only two people can play the game at the same time. That means that only 5 games will be played by 5 pairs?... Right?

- Thu Sep 11, 2014 11:46 am UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Re: Prisoners and their enemies

Cauchy wrote:The algorithm doesn't necessarily produce a maximum cut. Instead, it produces a sort of maximal cut, maximal in the sense that it cuts more edges than the cuts produced by flipping any one vertex to the other side. It's a local max, but not necessarily a global max.

Indeed. My mistake

- Wed Sep 10, 2014 9:22 am UTC
- Forum: Language/Linguistics
- Topic: Spelling out numbers in different languages
- Replies:
**19** - Views:
**8682**

### Re: Spelling out numbers in different languages

Vo2max wrote:In Welsh, dau (2) and wyth (8). Beyond 10 there are spaces.

Shouldn't there be numbers lexicographically bigger than wyth, then? 8000? 88?

- Wed Sep 10, 2014 9:16 am UTC
- Forum: Language/Linguistics
- Topic: Spelling out numbers in different languages
- Replies:
**19** - Views:
**8682**

### Re: Spelling out numbers in different languages

In Finnish, biljoona (1.000.000.000) and yksitoistatuhattayhdeksänsataayksitoista (11.911). Curiously, the alphabetically dead last number word in the language, integer or not, is the one for infinity (äärettömyys). Is bilijoona correct on its own? In English (and many other languages) you must say...

- Wed Sep 10, 2014 7:56 am UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Re: Prisoners and their enemies

Your method has the benefit of being complete after #prisoners time (I think), whereas finding a max cut is probably not doable in poly time (it is doable iff P=NP). Well, for max enmity (every prisoner has three enemies), my method produces a max cut, since only a max cut is a solution in this cas...

- Tue Sep 09, 2014 11:44 am UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Re: Prisoners and their enemies

Actually I agree with it completely now. Any maximum cut solves it. Funny. I hadn't thought of that :) My solution doesn't use graphs at all. What does your solution look like? Put all prisoners in the two blocks at some random configuration. Take one prisoner with 2 or more enemies in his block an...

- Mon Sep 08, 2014 3:53 pm UTC
- Forum: Language/Linguistics
- Topic: Spelling out numbers in different languages
- Replies:
**19** - Views:
**8682**

### Re: Spelling out numbers in different languages

In German, there is 12 = zwölf = zwoelf > zwei Also, in the (low (10^(3n) range, such as million, billion, trillion (!!!)), in German we have (10^18=)Trillionen>Trilliarde>Tausend I don't know the names for greater than Quintillionen, so I have to assume that this is the upper bound. So, the upper-...

- Mon Sep 08, 2014 10:02 am UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Re: Prisoners and their enemies

Actually I agree with it completely now. Any maximum cut solves it.

Funny. I hadn't thought of that

My solution doesn't use graphs at all.

Funny. I hadn't thought of that

My solution doesn't use graphs at all.

- Mon Sep 08, 2014 9:21 am UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Re: Prisoners and their enemies

Actually, never mind. This wasn't a maximum cut.

It really seems that a maximum cut does solve it, but I'm still not sure that ANY maximum cut does.

It really seems that a maximum cut does solve it, but I'm still not sure that ANY maximum cut does.

- Mon Sep 08, 2014 9:14 am UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Re: Prisoners and their enemies

notzeb wrote:Any maximal cut solves the problem...

Here is a max cut on a Petersen graph. Notice the prisoner with two enemies in his block.

- Sun Sep 07, 2014 11:05 pm UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Re: Prisoners and their enemies

What do you mean by this? Also, if you just max out the enmity you end up with a tetrahedron. If by "maxed out enmity" you mean that every prisoner has three enemies, then that's not true. Every even number of prisoners greater than or equal to four can have maxed out enmity. Not just ...

- Sun Sep 07, 2014 9:37 pm UTC
- Forum: Language/Linguistics
- Topic: Spelling out numbers in different languages
- Replies:
**19** - Views:
**8682**

### Spelling out numbers in different languages

A couple of friends and me played a game where we tried to imagine if we had all the integers spelled out and sorted in a lexicographical order, which would be the first and last in the list. We're Bulgarian and we played the game in Bulgarian, but we had fun playing it in other languages too. So he...

- Sat Sep 06, 2014 9:02 pm UTC
- Forum: Logic Puzzles
- Topic: Prisoners and their enemies
- Replies:
**21** - Views:
**6287**

### Prisoners and their enemies

Each prisoner in a prison has up to three enemies. If two enemies face each other, nothing serious will happen, because the odds of winning in a fight would be even, but if a prisoner faces two or three of his enemies, they'll team up, beat him, and quite possibly kill him. The guards know about thi...

- Wed Feb 19, 2014 1:49 pm UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

Can you tell us the answer? To what? If it's about the original question, ralphmerridew and sfwc answered in the frist couple of posts. If it's about the extended question: What the minimal set size Bob can achieve if Alice is allowed at most k consecutive lies, then I'm afraid I don't have it. The...

- Sat Jan 04, 2014 3:30 pm UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

Yeah... actually that was my bad. I forgot to mention that they need to be yes or no questions. I got this problem from a friend of mine, who apparently got it from the IMO 2012 set, where it's explicitly stated that the only possible type of questions is "Is your number in the this set?...&quo...

- Mon Dec 30, 2013 2:56 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1310: Goldbach Conjectures
- Replies:
**65** - Views:
**14032**

### Re: 1310: Goldbach Conjectures

Actually by reducto ad absurdum the Tautological Conjecture is true.

It should be referred to as the Tautological Theorem from now on

It should be referred to as the Tautological Theorem from now on

- Fri Dec 20, 2013 12:59 pm UTC
- Forum: Logic Puzzles
- Topic: Sum of three cards game
- Replies:
**6** - Views:
**4393**

### Sum of three cards game

Alice and Bob play a game: Nine cards with the integers from -4 to 4 are placed on the table (the numbers on the cards are visible to the players). Then Alice and Bob take turns in taking a card, starting with Alice (because she's a lady). When one of them has three cards which have numbers that sum...

- Wed Dec 11, 2013 4:18 pm UTC
- Forum: Logic Puzzles
- Topic: Flipping 50 consecutive cards
- Replies:
**15** - Views:
**5749**

### Re: Flipping 50 consecutive cards

I'm not sure how to prove it yet, but it seems to me that each player would be able to force an endless game. As for the winning conditions, they're the same as in jedelmania's solution: If the game doesn't become endless, for k < 50, if the initial number of cards is odd*50+k the first to play ...

- Wed Dec 11, 2013 6:28 am UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

From the IMO solution pdf

Minimum s (size of Bob's last set) for a given k (max number of lies for Alice):

Nothing about their algorithm though.

Minimum s (size of Bob's last set) for a given k (max number of lies for Alice):

A computer search shows that [s] = 2, 3, 4, 7, 11, 17 for k = 1, 2, 3, 4, 5, 6

Nothing about their algorithm though.

- Tue Dec 10, 2013 8:27 pm UTC
- Forum: Logic Puzzles
- Topic: Flipping 50 consecutive cards
- Replies:
**15** - Views:
**5749**

### Re: Flipping 50 consecutive cards

Does it change anything if the two players are sitting on opposite sides of the table? I.e., Card 1 for player A is card N for player B and each one flips 50 cards to their respective right? Is it profitable to stalemate? Edit: Changed "Is it possible to stalemate?" to "Is it profita...

- Tue Dec 10, 2013 7:04 pm UTC
- Forum: Logic Puzzles
- Topic: Flipping 50 consecutive cards
- Replies:
**15** - Views:
**5749**

### Re: Flipping 50 consecutive cards

And that is correct.

There is another solution that is a bit simpler. Should I post it?

There is another solution that is a bit simpler. Should I post it?

- Tue Dec 10, 2013 2:15 pm UTC
- Forum: Logic Puzzles
- Topic: Flipping 50 consecutive cards
- Replies:
**15** - Views:
**5749**

### Re: Flipping 50 consecutive cards

Adding to the last comment, n=100 also is a winning start, with the winning move to flip number 2. This forces the second player to flip 1 (only legal move) and effectively reduces the board to n=99. For me, the next step seems to be finding a losing start at all - I can conceptualize it, b...

- Mon Dec 09, 2013 3:53 pm UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

What about questions like that: Did you answer the previous question truthfully? Did you answer the previous n quesions truthfully? Do the last n answers contain more than m lies? Maybe a strategy can be made from chaining questions of that type? Well why don't you think it can be reduced like that...

- Mon Dec 09, 2013 3:02 pm UTC
- Forum: Logic Puzzles
- Topic: Flipping 50 consecutive cards
- Replies:
**15** - Views:
**5749**

### Re: Flipping 50 consecutive cards

jaap's interpretation is correct. If the leftmost card is face down and there are at least 49 cards to its right, it's a legal move to flip those fifty. Hence the requirement to have the last move be such that it leaves the first 1355 cards face up. Any other configuration of them and there will exi...

- Mon Dec 09, 2013 12:05 pm UTC
- Forum: Logic Puzzles
- Topic: Flipping 50 consecutive cards
- Replies:
**15** - Views:
**5749**

### Flipping 50 consecutive cards

Two people are playing a game. 1404 cards (27 decks) are placed face down in a row. When a player has their turn, they need to choose 50 consecutive cards for which the first (the left-most) one is face down and flip them. If a player has no legal move, they lose. That happens only if the first 1355...

- Sun Dec 08, 2013 8:37 am UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

Thoughts on Alice's strategy: She, like Bob, can determine if a number is eliminated. So let's call the set of n numbers that aren't eliminated C (as in candidates) = {c1, c2, .... cn } After every answer of hers she can calculate the number of consecutive lies she has told had her n...

- Sat Dec 07, 2013 8:48 am UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

Indeed. @Lopsidation It seems that 3 is the minimum value of s for k=2 @Nitrodon Are you trying to prove that Bob can always be certain to have Alice's number is a set of 2^(k-1)? That's not true. For sufficiently large k I can prove that x^k <= s <= 2^k, for any 1 < x < 2. Plus as I...

- Fri Dec 06, 2013 4:29 pm UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

about the solutions They Seem legit. My solution is (imo) a bit easier to explain but it's slower, because it always eliminates a single candidate number per 10 to 19 questions, while both of yours can eliminate multiple candidates We are left with the following obvious question: what is...

- Fri Dec 06, 2013 2:20 pm UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

Answering in a way that's logically false.

Her head explodes (along with the prize) on paradoxical questions so they aren't allowed.

Her head explodes (along with the prize) on paradoxical questions so they aren't allowed.

- Fri Dec 06, 2013 2:00 pm UTC
- Forum: Logic Puzzles
- Topic: Find a set of numbers containing mine
- Replies:
**32** - Views:
**9983**

### Re: Find a set of numbers containing mine

It is allowed, but if Alice simply alternates truth and lie it won't help you. She's not allowed to tell 10 lies in a row. That's it. She may tell truths and less than 10 lies in a row as much as she pleases. So suppose you get "no, no, yes, yes, yes, no, yes, no yes, no" to your repeated ...