## Hard Brain Teaser, THE PILL PROBLEM

Clarence has to take 2 different kind of pills (Pill A, Pill B). Both pills look exactly the same (same weight, color, shape, size, etc….

If he takes more than 1 pill of the same kind per day, he will die. Furthermore, if he doesn’t take 1 Pill A, and 1 Pill B every day, he will also die.

Clarence is on a limited budget, and since the pills are extremely expensive, he can’t throw any of them away.

One day, he got distracted and by mistake put 3 pills on the table. Since both pill types look identical, he’s not sure which pill is which.

**Question: How can he manage to take the pills without any further dire consequences and yet save the extra pill?**

Hint: you have the 2 jars of pills, with all the typical information a jar of pills gives you.

Thanks to Suineg for submitting! Next week, we have one from BobotheBear, and after that, Bilbao returns for some more challenges!

amboutwe| PUZZLE MASTER | Profile September 1st, 2010 - 4:57 amSplit each pill on the table in half. Combine left sides of each pill into one pile. Combine right sides of each pill into a separate pile. Take another pill from bottle A (assuming he poured from bottle A first – otherwise he’d have to count the pills to determine which bottle is has one pill missing verses two) and split in half. Add the left side to the left pile and right side to the right pile. This would give him two full pills of each so he can take one pile now and the second pile the next day.

joe| Profile September 1st, 2010 - 6:22 amI would take a pill out of the bottle that has one more and put it toether with the three others. GRind them down to a fine powder, mix well and divide exactly into 2. You would then take one pile each day for the two days…

Im back (and probably with the not quite right answers again.. :bash))

Love the new site!

Shawn| PUZZLE GRANDMASTER | Profile September 1st, 2010 - 8:02 amClarence is taking one of each pill every day, so the number of pills remaining in each bottle should be lower than the original number by the same amount. The bottle from which the extra pill was taken must be missing more pills than the other bottle, so Clarence can determine which type of pill the extra third pill is.

Example:

Pill A: bottle was filled with 60 pills, now contains 40, so 20 pills have been removed

Pill B: bottle was filled with 100 pills, now contains 79, so 21 pills have been removed

Clarence now knows that he is holding 1 A pills and 2 B pills

– Take (1) Pill A from the bottle and add it to the 3 unknown pills. You now have (2) Pill A and (2) Pill B in your pile.

– Take each of the 4 pills and cut them in half.

– For each pill, put one of the halves in a pile on the right and one of the halves in a pile on the left.

– Each pile now contains 2 halves of Pill A and 2 halves of Pill B, which is the same as (1) Pill A and (1) Pill B in each pile.

And Clarence lives to medicate another day!!

Hex| PUZZLE MASTER | Profile September 1st, 2010 - 8:48 amFrom the jars, we can know the number of A and B pills in the set of 3 pills:

A B

0 3: Straight forward

1 2: Add 1 x A pill and resort to pill splitting or other

2 1: Add 1 x B pill and resort to pill splitting or other

3 0: Straight forward

The pills can be split in half if they are tablets, or in the case of capsules can be emptied and split in half by weight. There may however be some medical restrictions where the tablets/capsules should not be split as the cover delays the ingestion of the medicine. RK can enlighten us more.

suineg| PUZZLE MASTER | Profile September 1st, 2010 - 11:00 am@Hex: you can safely assume that the tablets does not have the restriction of the cover, cool man.

suineg| PUZZLE MASTER | Profile September 1st, 2010 - 11:02 am@Shawn: How sad that sound!!!, “live to medicate foor another day” jajajaja, cool.

Bobo The Bear| PUZZLE MASTER | Profile September 1st, 2010 - 11:57 amFirst, count the pills left in each bottle. Then you’ll know if you have 2A and 1B, or 2B and 1A (You might have 3A or 3B, which would make the solution trivial).

Second, take out another pill from the bottle that contains more. This will ensure that you now have 2A and 2B.

Next, use a pill splitter to split each pill. For each pill, take one half immediately, and save the other half for tomorrow.

This solution rests on far too many assumptions for it to be useful in a practical setting. DO NOT FOLLOW THESE INSTRUCTIONS WITH REAL LIFE-SAVING MEDICATION. Always consult your health care provider with any issues regarding your medication.

Shawn| PUZZLE GRANDMASTER | Profile September 1st, 2010 - 1:01 pmWell-stated, Dr. Bobo.

For example, what if Clarence started on one medication, and then his doctor added the second medication at a later date. It is then possible that a certain number of Pill A has been taken prior to Clarence beginning to take Pill B. If Clarence doesn’t know FOR SURE how long he has taking Pill A, then the counting method won’t work and Clarence has a 50/50 chance of dying tonight. Better to discard the 3 pills and try to be more attentive in the future.

Bobo The Bear| PUZZLE MASTER | Profile September 1st, 2010 - 1:17 pm@Shawn: Good job on not assuming that bottle A and bottle B start off with the same number of pills. In your example, though, the line “the number of pills … by the same amount.” assumes that bottle A and bottle B were started on the same day (as in the beginning of a prescription). If these are refills, it may not be so easy, because the bottles are started on different days.

For example, if the medication was started 365 days ago, then:

Bottle A (60 per bottle) would be 5 days into new bottle, and should have 55 left.

Bottle B (100 per bottle) would be 65 days into new bottle, and should have 35 left.

You can still figure it all out, but the math would be slightly more difficult. Considering how easily distracted Clarence is with his live-saving medication, this might be beyond his abilities.

Bobo The Bear| PUZZLE MASTER | Profile September 1st, 2010 - 1:24 pmYou gotta live it when messages say the same thing at the same time, and cross paths like that.

Shawn| PUZZLE GRANDMASTER | Profile September 1st, 2010 - 1:50 pmBobo, we’re generally on the same page, you and I.

Shawn| PUZZLE GRANDMASTER | Profile September 1st, 2010 - 5:29 pmOf course, since Clarence must take one of each pill every day, we can probably readily assume that the doctor would have prescribed equal amounts of the pill, and done so at the same time. It is doubtful that there would have been a time at which only one of the pills would serve the purpose, and then suddenly a second pill was required in conjunction with the first in order to avoid death. In all likelihood, each bottle should contain the same number of pills on any given day.

suineg| PUZZLE MASTER | Profile September 1st, 2010 - 7:01 pmNice so nice man, you always surpass all my expactations, very cool!!!

suineg| PUZZLE MASTER | Profile September 1st, 2010 - 7:02 pmExpectations I meant, thats why I never post in the verbal games, so dislexic

Hex| PUZZLE MASTER | Profile September 2nd, 2010 - 2:43 pmTo cut short any further speculation, we can buy the 3 pills from Clarence and save him the aggravation

engjs1960| Profile September 2nd, 2010 - 7:46 pmIf he takes one of each each day, he can find out what pills he has by counting what’s left in each bottle. If the three pills are the same kind put them back in their bottle and start again.

So assume there are 2 of A and 1 of B. Add a B pill to the mixture. Break each pill into 2 equal parts. Take half of each of the four pills today, and the other half of each tomorrow.

Hedaiet El-Sabbahy| Profile September 21st, 2010 - 6:48 am* Take one pill from the bottle which’s having more one.

* separate the four pills from each other and split each into halves.

* take one half of each pill and drink the four halves together.

* then you’ll be taken one pill of each kind whatever the kind was.

* hope the man gets recovery from that desease which made all of us think a lot for solving the problem soon.

Hendy| Profile October 11th, 2012 - 10:36 pmI prefer the “Russian Roulette” answer. Take two pills and call me in the morning. If he calls, it would be to the doctor. If he does not call, it would be to the mortician.

:0)