# Pill problem

#### paulmdrdo

##### Active member
The doctor told you to take 2 different kind of pills (Pill A, Pill B) for ten days everyday. Both pills look exactly the same (same weight, color, shape, size, etc….
If you take more than 1 pill of the same kind per day, you will die. Furthermore, if you do not take 1 Pill A, and 1 Pill B every day, you will also die.
One day, you got distracted and by mistake put 3 pills on the table 2 B pills and one A pill and you don't know which is which.

How can you survive?

I've already searched for the solution to this problem.
Adding 1 pill A to the 3 unknown pills and split each pill in half. Thus having a balanced dose.
Half of those you take and save the other half for the next day.

I still dont get it. Because there is still a posibility that I might take more dose of one pill than the other.

What you think?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Hi paulmdrdo !

So we have 2 pills A and 2 pills B and do not know which is which.
If we take half of each pill and discard the other half, we will have 2 half pills A and 2 half pills B, won't we?
Swallowing all of those gives us 1 dose of pill A and 1 dose of pill B.

#### paulmdrdo

##### Active member
Hi paulmdrdo !

So we have 2 pills A and 2 pills B and do not know which is which.
If we take half of each pill and discard the other half, we will have 2 half pills A and 2 half pills B, won't we?
Swallowing all of those gives us 1 dose of pill A and 1 dose of pill B.
We have 4 pills in total. Splitting each pill into half we will have 4 half B pills and 4 half A pills. Since we dont know which is which, there is a posibility that you might take 3 half pills B and 1 half pill A or 3 half pills A and 1 half pill B or 4 half pills B or 4 half Pills A.

#### caffeinemachine

##### Well-known member
MHB Math Scholar
We have 4 pills in total. Splitting each pill into half we will have 4 half B pills and 4 half A pills. Since we dont know which is which, there is a posibility that you might take 3 half pills B and 1 half pill A or 3 half pills A and 1 half pill B or 4 half pills B or 4 half Pills A.
We have a total of $4$ pills. When we divide a pill in half, we keep one half with us and give the other half to our friend. We do this one by one for each pill. In the end we will be left be two halves of pill A and two halves of pill B.