### Brain Teasers

# Watery Drink

Mad Ade is stranded on a desert island (much to the relief of many). Other than just water, all he has to drink is a 20oz bottle of cola.

To conserve his luxury cola he decides that on the first day he will drink one oz and then refill the bottle back up with water. On the 2nd day he will drink 2oz and refill the bottle. On the 3rd day he will drink 3oz and so on...

By the time all the cola is gone, how much water has Mad Ade drunk?

To conserve his luxury cola he decides that on the first day he will drink one oz and then refill the bottle back up with water. On the 2nd day he will drink 2oz and refill the bottle. On the 3rd day he will drink 3oz and so on...

By the time all the cola is gone, how much water has Mad Ade drunk?

### Answer

Mad Ade has drunk 190oz of water.It is given that the Mad Ade has 20oz bottle of Cola.

Also, he will drink 1oz on the first day and refill the bottle with water,

will drink 2oz on the second day and refill the bottle,

will drink 3oz on the third day and refill the bottle,

and so on till 20th day.

Thus at the end of 20 days, he must have drunk

(1 + 2 + 3 + 4 + ..... +18 + 19 + 20) = 210oz of liquid.

Out of that 210oz, 20oz is the Cola which he had initially.

Hence, Mad Ade must have drunk 190oz of water.

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## Comments

ooooooooh

aaaaaaaah

Friedrich Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101 (at an early age of 9). Later on he found out: 's=n(n+1)/2'. With mad-ade's numbers: 20 x 21 / 2 = 210. Subtract the cola and you get the result of 190oz of water.

Also, unexplained in the answer but, I think, worth pointing out, is that there will always remain a fraction of the coke left, assuming complete mixing of the water added with the current contents of the bottle, until such time that the entire bottle is emptied. This, as stated, takes place on the 20th day.

Think how much water was put in.

0 on the first day

1 oz on the second day etc

19 on the 20th day when the complete bottle is drunk.

He drank all of it so S = 1 + 2 + ... + 19 =

19/2(19 +1) = 190 by Gauss' s method.

0 on the first day

1 oz on the second day etc

19 on the 20th day when the complete bottle is drunk.

He drank all of it so S = 1 + 2 + ... + 19 =

19/2(19 +1) = 190 by Gauss' s method.

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