The Simplified Pill Algorithm


Ok so I had to take one pill every day, and fortunately the pill package was marked, it contained 14 pills with labels Sunday, Monday and so on. It started with Sunday, which was the mark for the leftmost pill. The pharmacy gave me 30 pills every month, two packages and 2 separately, which meant that taking the pills would be out of synchronization. 

However, I had it all figured out: All I need is to remember a single number between -3 and 3 for the entire four weeks. Say the starting day is Tuesday. Then I had to remember the number -2. On Tuesday I take the leftmost pill for Sunday, on Wednesday I take the pill for Monday, on Thursday I take the pill for Tuesday,  and so on. If, for example, the starting date is Thursday, then I have to remember +3. The pill for Sunday I take on Thursday, and then the pill for Monday I take on Friday etc. Easy. (I tried to write this number of the package but this didn’t work.)

I can remember several 7 digit phone numbers so, in theory, I did not see any difficulty in remembering one small integer number for an entire month. The math itself was not too challenging.  

In practice it did not work so well. Sometimes I could not remember: either I already took the pill and the magic number is 2 or I did not and it is 3. Other times, I wondered if the magic number +2 or -2.

After several months I shared the problem with my wife. She listened with patience to my description and complaints and then had a suggestion which I quickly realized to be considerably better than my own method. “Perhaps it is not that important to start in the left corner,” she said, “If you have to start the package on Tuesday, you can take on Tuesday the pill for Tuesday, then continue and take on Wednesday the pill for Wednesday, and so on. If you start on Thursday, you can go ahead and take the pill for Thursday on Thursday, and if the first day is Sunday then you can start by taking the pill for Sunday!”




I'm An Idiot


I’m An Idiota comic from xkcd

This entry was posted in Mathematics to the rescue, Taxi-and-other-stories. Bookmark the permalink.

3 Responses to The Simplified Pill Algorithm

  1. jozsef says:

    Well, you still have to be careful. What would you do if you take the last pill of the leaf of tablets on Sunday?? You take it and after a few minutes/hours you won’t remember that. So you open the new box to take your regular Sunday pill…
    Those Sunday pills are troublemakers! And probably by now you see that there are more troublemakers around.

  2. Gil Kalai says:

    Dear Jozsef, yes indeed. This remind me of the well-known “absent-minded driver paradox” by Michele Piccione and Ariel Rubinstein; There was an entire volume 20 of Games and Econ Behavior devoted to papers about this game and many of those can be found online. Look here:

  3. Pingback: Updates and plans III. | Combinatorics and more

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