Author Topic: Trivia  (Read 1340 times)

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Online livo

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Trivia
« on: June 15, 2020, 11:55 AM »
An empty one.
Whiskey is the answer, but what was the question?

Online Peripatetic Phil

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Re: Trivia
« Reply #1 on: June 15, 2020, 12:32 PM »
Which set me thinking.  It won't (of course) be completely empty, because there will be air inside, but we have a saying — "empty vessels make the most sound".  Is this statement correct ?  If the vessel were completely empty (i.e., contained a perfect vacuum), would its sides still be able to resonate when struck ? 

And yes, Covid-19 lockdown is probably getting to me — I spent much of the last 48 hours working on the egg-dropping problem, first for two eggs, and more recently for three and more :

Quote
It is desired to know from the windows of which floor(s) (if any) in a 36-storey building it would be safe to drop eggs, and from which floors an egg would break were it to be dropped. The following assumptions are made :

     * An egg which survives a fall can be used again, and is not weakened in the process.
     * A broken egg must be discarded.
     * The effect of a fall from a given height is the same for all eggs.
     * If an egg breaks when dropped, then it would have also broken had it been dropped from a higher floor.
     * If an egg survives a fall, then it would also have survived had it been dropped from a lower floor.
     * A fall from a ground-floor window might break eggs, and it is equally possible that eggs could survive a fall from the top floor.

If only one egg is available and we wish to be certain of obtaining the correct result, the experiment can be carried out in only one way. Drop the egg from a ground-floor window; if it survives, drop it from a first-floor window. Continue upward until it breaks. In the worst case, this method will require 36 droppings.  But suppose 2 eggs are available — what is the smallest number of egg droppings that is guaranteed to find the solution ?
« Last Edit: June 15, 2020, 12:43 PM by Peripatetic Phil »
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Online Garp

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Re: Trivia
« Reply #2 on: June 15, 2020, 09:49 PM »
Wish we had a global moderator who could remove this rubbish.

Online livo

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Re: Trivia
« Reply #3 on: June 15, 2020, 10:06 PM »
With 2 eggs. Drop egg #1 from floor 18. If egg #1 breaks use egg #2 starting from the ground up to possibly floor 17, being possibly 18 drops.  If egg #1 survives you could just work upwards, possibly another 18 drops, or 19 in total, but you don't need to as you can again split and go to floor 27, but the worst case is the broken egg #1 from floor 18, so the answer is 18.
With 3 eggs. Drop egg #1 from floor 24. If egg #1 breaks use egg #2 from floor 11. If egg #2 breaks, use egg #3 from ground up being possibly 10 drops. If egg #2 doesn't break you still have 2 eggs and the answer is between floors 12 and 23. If egg #1 doesn't break you still have 3 eggs and the answer is between floors 25 and 36. The worst case is egg #2 broken from floor 11 so the answer is 12. (or maybe 10)
With 4 eggs. Drop egg #1 from floor 27. If it breaks drop egg #2 from floor 13. If it breaks drop egg #3 from floor 7. If it breaks then there are possibly 6 drops with egg #4 from the ground up.  The answer is 9. (or maybe 6 or 7)
The pattern appears to suggest the answer is the number of floors divided by the number of eggs (or not). But is it? What happens if you have 3 dozen eggs?
« Last Edit: June 16, 2020, 03:27 AM by livo »
Whiskey is the answer, but what was the question?


Online Peripatetic Phil

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Re: Trivia
« Reply #4 on: June 16, 2020, 10:16 AM »
Wish we had a global moderator who could remove this rubbish.

I believe there is one, Garp.  Why don't you use the "report to moderator" feature, explaining which the thread should be removed, and I am sure it will receive the attention that it deserves.
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Online Peripatetic Phil

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Re: Trivia
« Reply #5 on: June 16, 2020, 10:22 AM »
With 2 eggs. Drop egg #1 from floor 18. If egg #1 breaks use egg #2 starting from the ground up to possibly floor 17, being possibly 18 drops.  If egg #1 survives you could just work upwards, possibly another 18 drops, or 19 in total, but you don't need to as you can again split and go to floor 27, but the worst case is the broken egg #1 from floor 18, so the answer is 18.
With 3 eggs. Drop egg #1 from floor 24. If egg #1 breaks use egg #2 from floor 11. If egg #2 breaks, use egg #3 from ground up being possibly 10 drops. If egg #2 doesn't break you still have 2 eggs and the answer is between floors 12 and 23. If egg #1 doesn't break you still have 3 eggs and the answer is between floors 25 and 36. The worst case is egg #2 broken from floor 11 so the answer is 12. (or maybe 10)
With 4 eggs. Drop egg #1 from floor 27. If it breaks drop egg #2 from floor 13. If it breaks drop egg #3 from floor 7. If it breaks then there are possibly 6 drops with egg #4 from the ground up.  The answer is 9. (or maybe 6 or 7)
The pattern appears to suggest the answer is the number of floors divided by the number of eggs (or not). But is it?

I regret that neither of your hypotheses are correct, Livo, although "start from floor 18" is where most analyses commence (at least, for those who have not encountered the problem previously).  What you will find, when you investigate "start from floor 18" further, is that there is another "natural" starting point, and when you investigate that one you will find that it too is sub-optimal.  Which will cause you to think "OK, if there is no 'natural' starting floor that is optimal, clearly the starting floor (and subsequent floors) must be found in another way".  And then you will be en route to the solution.  As to three eggs or more, that one took me a further day to find, but it is now found and the method will generalise to $n$ eggs, for $n <= floors$.

Only one person (in my circle of correspondents) has come up with the correct answer for two eggs, and he admitted he had seen the problem before and had solved it by writing a computer program !  He also offered an answer for three eggs, which was wrong, but the error could have been no more than a simple typo.

** Phil.
« Last Edit: June 16, 2020, 11:02 AM by Peripatetic Phil »
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Re: Trivia
« Reply #6 on: June 16, 2020, 03:49 PM »
Livo's next reply (which contains the solution for E=2, F=36), and my comments thereon, have been moved to https://www.curry-recipes.co.uk/curry/index.php?topic=15503.0 so that those who want to try the problem for themselves can avoid reading the solution in advance.

** Phil.
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Online George

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Re: Trivia
« Reply #7 on: June 16, 2020, 11:10 PM »
Wish we had a global moderator who could remove this rubbish.

I couldn't agree more. Admin needs to get a grip. The forum is in danger of becoming little more than a dialogue between probably the current two most prolific posters, Phil and Livo. For the rest of us it's so incredibly boring unless, like these two, you enjoy reading absolute drivel.

Online livo

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Re: Trivia
« Reply #8 on: June 17, 2020, 07:15 AM »
Wish we had a global moderator who could remove this rubbish.

I couldn't agree more. Admin needs to get a grip. The forum is in danger of becoming little more than a dialogue between probably the current two most prolific posters, Phil and Livo. For the rest of us it's so incredibly boring unless, like these two, you enjoy reading absolute drivel.

This area of the forum is titled "Talk about anything other than curry", which incidentally features pretty close to the top and has the description "Here is the place to talk about everything that is not curry related, news, sports, tv, fishing, wallpaper, car trouble....come on you know you want to....."

Data flow and guest traffic visiting the site is what matters to Admin, I'd wager.  Who is forcing you to read it?  The description above mentions TV and sports. Is throwing bricks at the TV instead of changing channels some new sports thing I've missed?
« Last Edit: June 17, 2020, 07:29 AM by livo »
Whiskey is the answer, but what was the question?

Online Peripatetic Phil

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Re: Trivia
« Reply #9 on: June 17, 2020, 09:08 AM »
The forum is in danger of becoming little more than a dialogue between probably the current two most prolific posters, Phil and Livo. For the rest of us it's so incredibly boring unless, like these two, you enjoy reading absolute drivel.

The solution, George, lies not in Yousef's hands but in your own, and those of every other silent member.  Write more.  Tell us about your recent adventures in BIR land.  Publish your recipes for chicken korma.  Discuss Syed's tremendous contribution to this arena.  Tell us which of his dishes you have tried and which you still intend to.  In other words, participate more, criticise less.

** Phil.
« Last Edit: June 17, 2020, 03:58 PM by Peripatetic Phil »
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