## Search found 24 matches

Fri Dec 28, 2012 7:49 am UTC
Topic: 1153: "Proof"
Replies: 64
Views: 18985

### Re: 1153: "Proof"

This reminds me of a historical Darwin Award winner : Clement Vallandigham was a well-known Northern Democrat who campaigned for states' rights during the Civil War. In 1863 Vallandigham was convicted of treason for his speeches attacking the administration of President Lincoln. He was banished to t...
Thu May 31, 2012 1:46 pm UTC
Forum: Logic Puzzles
Topic: Seventeen "Blue Eyes" Objections and Responses [SPOILER]
Replies: 73
Views: 41568

### Re: Seventeen "Blue Eyes" Objections and Responses [SPOILER]

I think I can come up with a quicker method, though. Instead of guessing randomly on Minute n, why not guess Color n on the first minute? The overall rate of success should be the same either way. Actually, this can even be improved. The signaller agrees to guess n immediately. Everyone else knows ...
Thu May 31, 2012 4:15 am UTC
Forum: Logic Puzzles
Topic: Seventeen "Blue Eyes" Objections and Responses [SPOILER]
Replies: 73
Views: 41568

### Re: Seventeen "Blue Eyes" Objections and Responses [SPOILER]

Ah, I wish I'd figured out how to get email alerts on threads here, or I'd have joined the conversation about Peeling's idea; oh well. It's a neat idea but doesn't work in relation to the puzzle as originally worded. The "aha" moment of the original puzzle is very sati...
Wed May 23, 2012 4:19 am UTC
Forum: Logic Puzzles
Topic: Another gambling puzzle
Replies: 7
Views: 6728

### Re: Another gambling puzzle

This is just a function of the casino's assets (A). Replace the expected returns with an upper bound: \begin{align*} E &= \sum_{k=1}^{\infty}\left(\frac{1}{2}\right)^k P \text{ for } \{P = 2^{k-1} \text{ when } 2^{k-1} \le A,\text{ otherwise } A\} \\ &= \sum_{k=1}^{\log_2(A)...
Sat May 19, 2012 5:35 am UTC
Forum: Logic Puzzles
Replies: 23
Views: 7248

The expected value function given in the OP is misleading because it only calculates the expected value of one round. In the iterated game the expected value quickly goes to "you'll loose everything" (remember a single loss at any point means you are bankrupt). When deciding how many roun...
Sat May 12, 2012 5:57 pm UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

If the economy of scale comes from having a single firm and not a single factory, why is it more efficient? If the firm has ten factories which are each the "right size" for economy of scale, why is it better to have one firm managing all ten factories and not ten firms each with one fact...
Sat May 12, 2012 8:28 am UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

There are lots of considerations here. You postulate a product for which economy of scale works. So the best approach is to have one single super-expensive factory which produces all of the product. But what happens if that factory gets bombed? What if it catches fire? Some ways it's more efficient...
Sat May 12, 2012 7:40 am UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

If we had claims against anyone ever doing anything which might possibly have any effect on us that we didn't like, we would have claims against anyone ever doing anything at all, since we all live in the same universe and every action has uncountable unforeseen consequences. This is the kind of sc...
Fri May 11, 2012 2:05 pm UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

Pfhorrest: You're still assuming away the problem. As soon as there's any interaction at all, the line between people's rights needs to be drawn, and you can't assume away any conflicts. Do you have the right to risk my life without my permission? Do I have the right to prohibit you from operating a...
Fri May 11, 2012 6:28 am UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

Precisely nothing. Which is why citizens, as shareholders in their government, have the moral responsibility to hold accountable the people in the government who authorize such actions. The three recourses available to a citizenry against a tyrannical government is the Ballot, the Bench, and the Bu...
Fri May 11, 2012 2:18 am UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

Since there are many fewer employers than there are employees, the employers have the negotiating advantage. Is there anything a free market can do about that? My own thought is to limit the size of corporations. Gradually reduce the maximum size -- first Walmart has to split up into smaller corpor...
Thu May 10, 2012 1:06 am UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

I tend to see it as, "Taxes are user-fees for civilization." The problem with this perspective is that we generally frown on being forced to buy someone's product. Imagine if your ISP wouldn't let you cancel their service and kept billing you for it whether you wanted it or not. AOL actua...
Wed May 09, 2012 3:10 am UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

So, according to Rand, not all evil stems from self-sacrifice, but also the belief that others can be sacrificed for your sake. Maybe it's because it's 1AM where you are and you didn't phrase this well, but if that's an accurate description, then we're back to saying that her work says nothing of s...
Sat May 05, 2012 11:39 pm UTC
Forum: Logic Puzzles
Topic: Puzzle
Replies: 7
Views: 3357

### Re: Puzzle

Yes, I solved your hint, and it clearly means something. But it doesn't seem like a satisfying solution to the puzzle to me, and you threw out a lot of information to find that, so I can't help but wonder if there's more there to be found. There might be more interesting stuff to play with in the d...
Fri May 04, 2012 1:06 pm UTC
Forum: Logic Puzzles
Topic: Puzzle
Replies: 7
Views: 3357

### Re: Puzzle

hint: 0-4 = white, 5-9 = black. Which "pixels" break the underlying pattern? That doesn't seem like it gives a whole answer to me, but I haven't found anything else yet. The converted image: http://i.imgur.com/3qtpa.png The squares that don't match the underlying checkerboard pattern:...
Fri May 04, 2012 12:21 am UTC
Forum: Logic Puzzles
Topic: Puzzle
Replies: 7
Views: 3357

### Re: Puzzle

hint:
Spoiler:
0-4 = white, 5-9 = black. Which "pixels" break the underlying pattern?
Mon Apr 30, 2012 2:10 pm UTC
Topic: 1049: "Bookshelf"
Replies: 867
Views: 135320

### Re: 1049: "Bookshelf"

edit: ninja'd
Sat Apr 28, 2012 6:02 am UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 47207

### Re: How many prisoners?

Nights 20-24: All the people that sent a signal on night 19, and received a signal every night since then, send a signal. This ensures that either a) the only people in the prison are P 1 , P 2 , P 3 or a P 4 and everyone knows it, therefore there are at most 6 people, this is scenario 5, or b) the...
Fri Apr 27, 2012 2:29 pm UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 47207

### Re: How many prisoners?

Nights 20-24: All the people that sent a signal on night 19, and received a signal every night since then, send a signal. This ensures that either a) the only people in the prison are P 1 , P 2 , P 3 or a P 4 and everyone knows it, therefore there are at most 6 people, this is scenario 5, or b) the...
Fri Apr 27, 2012 12:43 am UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 47207

### Re: How many prisoners?

It isn't possible for a prisoner to receive their own message. The reason is that the prisoners are not moved between the sending and the receiving of the messages. Instead, the rearrangement of the prisoners happens after one day's messages have all been received but before the next day's messages...
Tue Apr 24, 2012 7:49 am UTC
Forum: Logic Puzzles
Topic: How many prisoners?
Replies: 112
Views: 47207

### Re: How many prisoners?

Impressively complicated solution, but in practice: If we have 16 prisoners (not unreasonable), the warden is strong enough that we can spend a lifetime playing this game, and have narrowed it down to somewhere in the 15 - 32768 range. I suppose it's progress. If we have 4 prisoners, an...
Sun Apr 22, 2012 4:16 am UTC
Forum: Logic Puzzles
Topic: Mental exercises to do while running
Replies: 4
Views: 6067

### Re: Mental exercises to do while running

It's more an exercise in memory than math, but when I was in high school, our baseball team started every practice during the preseason with a 2.5 mile run. Each day I'd pick a new odd number and see how many times I could double it before getting back to the field. Obviously the challenge is to kee...
Tue Apr 17, 2012 6:11 am UTC
Forum: Logic Puzzles
Topic: x^x^x^x^x=5?
Replies: 30
Views: 12615

### Re: x^x^x^x^x=5?

I'm betting, instead, that the x^s are supposed to be infinite. In other words, solve x^(x^(x^(x^(x^(.....))) = 5. The simple trick is realizing that the infinite exponentiation also equals x raised to the same infinite exponentiation. Thus, the general solution: x^(x^(x^(x^(...)...
Tue Apr 17, 2012 5:32 am UTC
Forum: Logic Puzzles
Topic: 100 Cards, and others
Replies: 9
Views: 5187

### 100 Cards, and others

Tried searching for various keywords and didn't see anything like this one. Fairly simple, but it's also fairly easy to tie yourself into knots trying to go down a wrong path, so I figured I'd post this one: 100 Cards with various visible values are laid out in a single file line. Two players will a...