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:

The answer is: 14

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!!

String around the Earth circumference Puzzle. If add some length how much hight it rises?



The Puzzle:

The circumference of the Earth is approximately 40,000 km. There is a string circles the Earth, touching the ground at all locations.
Now if you add just 10 meters to its length, How far will it rise above the ground.

I know your guess would be that it will still graze the surface of earth. The raise would be infinitesimally small. But think again that could a fly,
an ant, or a man squeeze underneath it.



Solution:
Let p be Pi=3.14159
Use the formula Circumference = 2 × p × R

Before Circumference = 2 × p × R
After Circumference + 10m = 2 × p × (R + Gap)

Subtracting the two:
10m = 2 × p × Gap

So, the Gap = 10m / (2 × p) = 1.6m approximately

So, a man could fit under it easily.


Voila!! This is amazing discovery. 

9999=4 8888=8 1919=? Numerical Counting Puzzle



Now there is a puzzle, which will shake you:
9999=4
8888=8
1816=3
1212=0
1919=?
Solve the puzzle.


Solution:
The puzzle needs you to calculate the number of circles in the numbers.

For instance - 9 has one circle in it. And then 8 has 2

Hence see as below:
9999=4 (each 9 has 1 circle)
8888=8 (each 8 has 2 circles so 2 x 4 = 8)
1816=3 (8 has one circle and 6 has 1 so 2)
1212=0 (no circles in 1 & 2)
Hence, 1919=2 ( 2 circles of the number 9)


I have also seen another solution. THough not a clean one, but still the logic doesnot smells so foul:
See, sum of 9999 is equal to 4. Therefore, each 9 is equivalent to 1.
See 1212 is equal to 0. So 1 and 2 are equivalent to 0.
Therefore, 1919 is (0+1+0+1), so it is equivalent to 2.


--Enjoy