## Monday, November 3, 2008

### The Pill Puzzle

You are on an unbelievably strict medical prescription. Every morning you have to take exactly one pill A and one pill B. You must keep this up for a month, or there will be dire consequences to your health. You have just enough pills to last you the month, and you can't afford to go to the pharmacist to get more.

And so, you are dismayed when halfway through the month, you make a mistake. Right after putting one of pill A in your hand, you accidentally poured two of pill B in your hand. The pharmacists apparently didn't have the foresight to make pills A and B different colors or anything. Now you have three indistinguishable pills in your hand, and you're not sure what to do with them.

How can you keep up with your prescriptions without having to go to the pharmacist to get more pills?

see the solution

Anonymous said...

Screw it. Just down both bottles with a fifth of Jack.

;-)

Yoo said...

Just take two pills at random, as both pills A and B are placebos sold by the evil pharmaceutical companies. ;)

(Just take pills as normal except for two days. For the two days, cut each of the indistinguishable pills in half, being very careful not to mix them up, cut the last remaining pill A into half, too, and take a half from each pill each day. Then you won't die ...)

Secret Squïrrel said...

Since you've already been a bit of a klutz, I think it's a bit risky to be cutting pills in half and hoping not to mix them up! What about simply biting each of the 3 pills in half and swallowing the part that's in your mouth? Then eat half of another 'A' pill. Pedantic, I know - but I prefer solutions that minimise the possibility of creating further problems.

If you're looking to extend the puzzle, some obvious ways of doing that are:

2. (Trivial) You have to take exactly 1 pill of 3 types each morning and accidentally pour out 2 of pill 'C' (into 1 each of 'A' and 'B').

3. (Not much harder) You have to take exactly 1 pill of 3 types each morning and pour out 1 of 'A', 2 of 'B', and 3 of 'C'.

4. You have to take 2 of pill 'A' and 3 of pill 'B' but instead pour out 3 of 'A' and 4 of 'B'.

miller said...

Puzzle variations! You're someone after my own heart.

Unfortunately, I think original puzzle was great because it required a "trick". The obstacle in coming up with a good variation is that it has to make use of a different trick.

Secret Squïrrel said...

Hmm, they were a bit lame.

How about you have 4 identical bottles of pills each with a different label. You know that none of the bottles are correctly labelled but that by opening up the bottles and looking inside, you will be able to tell which pills are which?

What is the minimum number of bottles you must open before you know what is in each bottle?

If you opened bottle 'A' and found that it contained 'C' pills, which bottle should you open next?

miller said...

Oh, that's cool. It's like the three-barrel puzzle (as I heard it, there were fish inside).