# Assignment No. 7.1

## Condition:

Professor Severus Snape has prepared three potions, each with a volume of 300 ml. The first potion makes the person who drinks it smart, the second makes them beautiful, and the third makes them strong. To ensure the potion works, one needs to drink at least 30 ml of it. Severus Snape was about to drink his potions when he was called to the headmaster's office and left, leaving the labeled potions in large jugs on his desk. Taking advantage of his absence, Harry, Hermione, and Ron approached the table with the potions and began to sample them.

Hermione was the first to try the potions: she approached the first jug with the potion of wisdom and drank half of it, then poured the remainder into the second jug with the potion of beauty, thoroughly mixed the contents, and drank half of it. Next, it was Harry's turn: he drank half of the third jug with the potion of strength, then poured the remainder into the second jug, thoroughly mixed everything in this jug, and drank half of it. Now all the contents were in the second jug, which fell to Ron. What percentage of the contents of this jug does he need to drink to ensure that each of the three potions will definitely affect him?
# Answer: 80

## Exact match of the answer -1 point

## Solution.

First, Hermione drinks $300 / 2=150$ ml of the wisdom potion, and then she pours 150 ml into the second jug, after which the second jug contains 150 ml of the wisdom potion and 300 ml of the beauty potion. When she drinks half of the contents of this jug, 75 ml of the wisdom potion and 150 ml of the beauty potion remain. Now it's Harry's turn. He drinks $300 / 2=150$ ml of the strength potion, and then he pours 150 ml into the second jug. There, it becomes 75 ml of the wisdom potion, 150 ml of the beauty potion, and 150 ml of the strength potion. When Harry drinks half of it, 37.5 ml of the wisdom potion, 75 ml of the beauty potion, and 75 ml of the strength potion remain. Now it's Ron's turn.

According to the problem, to make the potion effective, it is enough to drink at least 30 ml of it. Therefore, Ron needs to drink at least 30 ml of the wisdom potion. Since the wisdom potion is the least in quantity, if Ron drinks 30 ml of it, he will drink more than 30 ml of the other potions. This means he needs to drink a portion of the jug equal to 30 ml / 37.5 ml * $100 \% = 80 \%$.