George Rebane
RR readers were introduced to the Split Pill Problem (SPP) in a passing Scattershots entry last summer. The problem involved giving our puppy Puna her pain meds after her second knee repair surgery, and that evoked an interesting problem the solution to which turned out to have several features which generalize to and can illuminate other realworld problems. Puna’s daily dose from the pill bottle was a half pill. If I shook out a whole pill, I would split it and give her a half, returning the other half to the bottle. On a day when a half pill emerged, I would just give the half.
The vet said to do that until the pill bottle was empty. Given the random way in which whole and half pills emerged, I wondered how soon could I expect to get to a day when only half pills remained in the bottle and I would no longer have to split pills. The solution turned out to be very interesting, which I have documented in a somewhat whimsical technical note that requires no math beyond grade school arithmetic to understand. You can access the pdf here – Download TN1910-1_Split Pill Problem Solved
I’ll leave you with a piece of eye candy from the report that illustrates the graphical beauty of the SPP solution where it will be fully explained. Enjoy.
rebanesruminations.com 
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