You have contracted a virus, and in order to survive you are told you must take exactly 1 A pill from one bottle and 1 B pill from another bottle at exactly noon every day for the next 10 days. If you miss a day or take more pills than prescribed you will not survive, and you can only take this 10 day course of pills once.

You take the pills as instructed for the first 2 days, on the third day a few minutes before noon you shake 1 pill A in to your hand, then inadvertently, you shake 2 B pills in to your hand, so you now have 3 pills in your hand that all look identical and you don't know which is which.

Can you survive? If so, how?

you ignore the pills in your hand, take 1 fresh pill from both bottles and then contact the pharmacy to get replacements.

Nice idea, but sorry you cannot obtain any more pills, you are only provided and allowed to have the correct number for the 10 day course, which cannot be repeated.

However, it does buy you a little more time to try and find find a solution.

I'd check my pharma guide
against the markings on the pills.

Pills are required to be stamped,
to identify what they are.

You count the pills left in the bottles to see which one is short a pill.

Keep the three separate for later, and take pills out of bottles as directed till one is left.
the 3 mixed pills are each halved, and the halves mixed up.
take the 1 remaining pill, and two random halves.
Then last time (if still alive), take all remaining halves.

Theory is I am much safer toward the end of the course if the pills do work;
second last dose is least likely (probability) to be two same pills - more chance to be half a pill wrong - may survive that day;

last dose must be correct, or only half a pill wrong, otherwise you would already be dead.


Or go to a music festival pill testing station, and see if they can tell the difference between the three.

You add another A pill, dissolve them in water, drink half today and drink half tomorrow.
Problem solved.

Thanks everyone for the replies, here is the solution.

You have in your hand 2 B pills and 1 A pill. You shake out another A pill from the bottle, so you now have 2 A pills and 2 B pills in your hand. (but you don't know which is which)

You cut a pill in half, take a half and put the other half aside for tomorrow, you do this with the four pills in your hand, so you have taken half of the pills in your hand, 1 A pill and 1 B pill and have saved the other 4 halves for tomorrow. You survive.

I think you were nearly all on the right track to the solution, I did not manage to get as near to the solution myself.