Topic: Trivia

[livo]

An empty one.

[Peripatetic Phil]

Which set me thinking.  It won't (of course) be completely empty, because there will be air inside, but we have a saying

[Garp]

Wish we had a global moderator who could remove this rubbish.

[livo]

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?

[Peripatetic Phil]

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.

[Peripatetic Phil]

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.

[Peripatetic Phil]

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.

[George]

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.

[livo]

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?

[Peripatetic Phil]

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.