# Making bucket empty with 50% take out rate puzzle

A bucket is full of water. 50% of the water is taken from it every hour.

How many hours will it take until it is completely empty?

Hint:- Answer is not infinite 🙂

The answer is 90 hours.

**EXPLANATION-**

Surprising as it may seem, the answer follows from the properties of matter and Avogadro’s number.

All the answers provided here so far assume that the bucket of water is infinitely divisible. But the fact is there comes a stage where you are left with just one molecule in the bucket. You cannot divide a single molecule any further without losing the property of water. It is a fundamental principle of chemistry. You stop when the bucket has just one molecule or you remove that one molecule also after one hour.

With that background, let us look at the calculations.

One mole of water weighs 18.015 grams.

One mole of water (any substance for that matter) contains 6.022 x 10^23 molecules (Avogadro’s number).

To keep the calculations simple, let us assume the bucket holds 36 litres or 36 kilograms of water (that is a reasonable size also).

36 kgs of water is equal to 2000 moles (approx).

2000 moles of water contain 2000 x 6.022 x 10^23 = 1.2044e+27 molecules.

hours Molecules

0 1.2044e+27

1 6.022E+26

2 3.011E+26

3 1.505E+26

.

.

.

87 7.783E+00

88 3.892E+00

89 1.946E+00

90 9.729E-01 (Note the sign has flipped from + to -)

You can also start with one molecule at zero hours, double the quantity every hour and see how long it takes to reach 1.2044e+27 molecules.

If you double the size of the bucket, the time goes up by one more hour.

Here is the python script that did the actual calculation:

molecules = 2000 * 6.022 * 10 ** 23

hours = 0

while molecules > 1:

molecules = molecules / 2

hours = hours + 1

print hours, ‘%.3E’ % molecules

**Source** – Quora

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Dr. Willam and surgical gloves puzzle

Dr.Willam wants to operate for three different persons who were wounded. But he had only two surgical gloves. There is ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### To which one will the needle touch 1 OR 2

In the gear arrangement, To which one will the needle touch, 1 OR 2Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Crossing the Bridge Puzzle (Bridge and torch problem)

A bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a ...Read More »### Probability of having boy

In a country where everyone wants a boy, each family continues having babies till they have a boy. After some ...Read More »### Magical flowers!!

A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »### How many times a day do all three hands of analog watch overlaps?

There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### Minimum number of persons needed to cross a Desert

In the middle of the confounded desert, there is the lost city of “Ash”. To reach it, you will have ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Overthrow your math teacher!

Some numbers are very mysterious. They are all integers. They have more than one digit. If you multiply them with ...Read More »