### Real Expensive Pills

You have Some Terminal Condition, which necessitates taking two pills a day:

one Pill A and one Pill B. If you neglect to take either pill, you die; if you take more than one A or more than one B, you die. If you don't take them at exactly the same time, you die.

This morning you are going through your usual routine. You pick up your bottle of A Pills and gently tap one into your palm. Then you pick up your bottle of B Pills and tap it, but two pills accidentally fall into your hand. You now hold three pills (one pill of A and two pills of B), you don't know which are which, and they are completely indistinguishable from each other. The A Pills are the same color as the B Pills, they are the same shape, same size - they are identical in every respect. Your doctor is charging you $10,000,000 a pill! So you dare not throw any away.

Thus, the puzzle: what can you do to ensure that you take only one A Pill and only one B Pill today, without wasting any pills (either today or in the future)?

Update (04/03/2010): Solution posted by Nikhil Pandey (CSE, IITB Alumnus and working at ASUS Taiwan) in comments!!

you were very foolish to tap out 2 tablets at once

ReplyDeletehowever do this now

take another pill A out......and take care not to take out 2 pills

now u have 2 pills A and 2 B pills

next aim divide 2 a and 2 b into one a and one b

powder all the 4 tablets mix them well and have half today half tomorrow

warning - if u can not mix well, then cut all 4 in half

have one half today...another tomorrow

@Pandey.. Nice solution..Thanx..

ReplyDeleteIf you follow the powdering approach, you will die with probability 1 :)

ReplyDeleteThat is because to not die, the mixture should have exactly equal proportions of A and B which is a possible but extremely improbable event(prob. = 0).

The deterministic solution is -

Take another A out. Now you have 2 As and 2 Bs. Cut each in half and keep the left halves and right halves separate. Eat the collection of left halves today and right halves tomorrow.

Now since I have brought extreme probabilities into picture, I should emphasize that please use an infinite precision scale to chop the tablets in perfect halves otherwise you are still probably dead :)