## Saturday, June 21, 2014

### Highest floor fall - Eggs not break Puzzle. It is a 100 floor building.

The Puzzle:

Determine the highest floor on a 100 floor building from which an egg may be dropped without breaking.

You are given two identical eggs, which you can drop from various floors of the building, to carry out your test.

Assume that, if the egg doesn't break after being dropped, it may be reused without suffering any loss of quality.
But if both eggs break before you have determined the highest floor, then you are over.

Find what is the least number of times you must drop the eggs in order to determine the highest floor?

Our Solution:

You drop the first egg from the 14th floor.
If it breaks, you can then determine the highest floor by dropping the second snooker ball no more than 13 times.
The above process would be to drop it from the 1st floor, and if it doesn't break, drop it from the 2nd floor, and if it still doesn't break, drop from the 3rd, etc
Hence, 13+1=14 chances

However, if the first egg survives the drop from the 14th floor, you then drop it from the 27th floor (14 + 13 = 27).
If it breaks, you can complete your test in no more than 12 drops with the second ball by dropping it between the floors 15 to 26.

Then, If from the 27th floor the first ball still doesn't break, the next floor to drop it from is the 39th (14 + 13 + 12 = 39).
If it breaks, drop the second ball from floors 28 to 38 (max 11 drops).

after the 39th floor should be the 50th floor (14+13+12+11),
then the 60th floor (14+13+12+11+10), and so on.

If the first ball survives 11 drops, you will be on the 99th floor. In that case, it only takes one more drop to complete the whole test.

So, this solves the puzzle.

Oh! stop. Think again!!!
You have just verified that 14 is the right answer. But how did one reached that answer?
Think again!!