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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 ?
Wish we had a global moderator who could remove this rubbish.
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?
Quote from: Garp on June 15, 2020, 09:49 PMWish 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.
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.