Puzzle challenges!

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Ravana
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Re: Puzzle challenges!

Post by Ravana » November 21st, 2017, 10:43 pm

Spoiler:

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GunChleoc
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Re: Puzzle challenges!

Post by GunChleoc » November 22nd, 2017, 6:19 pm

Correct! :)
Spoiler:

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Re: Puzzle challenges!

Post by Samonella » June 12th, 2018, 3:14 am

Time to bring the puzzle thread back to life, at least for a little while! Here's a puzzle that some of my friends were surprised I hadn't heard before, apparently it's a classic.

In front of you are two fuses, both a meter long, and a lighter. You know that if you lit one end of either fuse on fire, it would take exactly one hour for the entire thing to burn away. Your task is to use these two fuses to measure exactly 45 minutes.

It sounds easy at first, but then you realize that the rate at which the fire spreads isn't known; maybe it will travel uniformly from one end to the other over the course of the hour, or maybe it will burn through 90% of the fuse in 10 minutes and slowly smolder through the remaining centimeters for the next 50. In other words, seeing when the fire crosses one's halfway point doesn't tell you that 30 minutes have passed. On top of that, the two fuses aren't identical, so watching one burn doesn't tell you anything about the other's rate. All you know for sure is that it takes an hour for the fire to get from one end to the other.

Measuring 45 minutes with nothing but two silly fuses and a lighter will take some creativity, but there is a good answer.
The last few months have been nothing but one big, painful reminder that TIMTLTW.

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Re: Puzzle challenges!

Post by Landiss » June 12th, 2018, 7:46 am

Samonella wrote:
June 12th, 2018, 3:14 am

In front of you are two fuses, both a meter long, and a lighter. You know that if you lit one end of either fuse on fire, it would take exactly one hour for the entire thing to burn away. Your task is to use these two fuses to measure exactly 45 minutes.
Spoiler:
It was nice puzzle, I didn't know it before.

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Re: Puzzle challenges!

Post by Samonella » June 12th, 2018, 10:49 pm

Yep, that's exactly right!

If anyone is interested, I found a place with several more good riddles: the TED talks youtube channel. Here is a link to the playlist. A lot of them are repeats of what's already in this topic (in fact a couple of the ones I posted a stolen straight from it) and some of them have silly think-outside-the-box answers that don't feel satisfying at all, but there are a decent amount of good, new ones. For example, the Seven Planets riddle, about halfway through the playlist, is really good.
The last few months have been nothing but one big, painful reminder that TIMTLTW.

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Re: Puzzle challenges!

Post by Inky » June 13th, 2018, 5:07 pm

Cool, it's great to see this thread again! :D

I've got a quick one:
You're getting dressed in the dark and want to put on a matching pair of socks. You know you have two piles, one with 1 black sock and 2 white socks, and another with 2 black socks and 2 white socks. (And of course, you can't tell the two colors apart in the dark.) You decide to choose a pile and then randomly choose 2 socks from that pile and wear them. Which pile should you choose to maximize your chance of getting a matching pair (or are they the same)?

See, this one has real world applications ;) :eng:

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Re: Puzzle challenges!

Post by Landiss » June 13th, 2018, 5:37 pm

Spoiler:

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Inky
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Re: Puzzle challenges!

Post by Inky » June 13th, 2018, 6:01 pm

That's mostly right, just a tiny mistake:
Spoiler:

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Re: Puzzle challenges!

Post by Landiss » June 13th, 2018, 6:05 pm

Ah yes, what a silly mistake. You are right.

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Re: Puzzle challenges!

Post by Inky » July 19th, 2018, 10:24 pm

I remembered another little probability problem so I'm using it as an excuse to revive this thread :whistle:

A and B are playing a game: A flips 101 fair coins, and B flips 100 fair coins. The person who gets the most heads wins.
Who do you think is more likely to win?

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Re: Puzzle challenges!

Post by WTrawi » July 20th, 2018, 7:27 am

I'm so glad this thread is back again :)
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lol I actually should replace this signature now

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Re: Puzzle challenges!

Post by Eagle_11 » July 20th, 2018, 11:36 am

B cause he has one unit smaller pool of probability to work with ?

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Re: Puzzle challenges!

Post by Inky » July 20th, 2018, 3:59 pm

I don't understand what you mean, but no it's not B - after all B has less coins total, and we're counting the total number of heads each person flips.

Here's a hint:
What about this game - A flips 101 fair coins, B flips 100 fair coins, and the person who gets the most tails wins?

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Re: Puzzle challenges!

Post by Samonella » July 21st, 2018, 1:19 am

Well it seems obvious that A would be more likely to win either game. I just think no one is brave enough to say it because these statistics questions always have some tricky, unintuitive answer. :roll: :lol:

But after all, it's the same as if A flipped 100 times and B only flipped 2; of course A is more likely to win. It isn't nearly as big of an advantage in the original question, but it's a small advantage for the same reason.
The last few months have been nothing but one big, painful reminder that TIMTLTW.

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Re: Puzzle challenges!

Post by Inky » July 21st, 2018, 3:05 am

EDIT: Ooooops I totally asked the wrong question...I completely forgot it's possible for neither person to win the game. That's what I get for posting from memory :doh: Of course your answer to the original question was right :oops:

What I should have asked was the probability A would win.
It turns out the probability A would win is 1/2 (kind of counterintuitive, since you'd think it'd be greater):
Spoiler:

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