[CrackMonkey] [schoen@loyalty.org: Pill-weighing]

[Seth David Schoen]

Based on Gardner's _aha! Insight_, if I remember correctly.  I've sent
Lise back to the grad students with the following counter-challenges:

----- Forwarded message from Seth David Schoen <schoen at loyalty.org> -----

[...]

You are a pharmacist, and [...]

(1) You have n bottles of pills.  Each bottle contains an unknown number of
pills.  The pills are supposed to be 100 mg, but one bottle is "bad": all
the pills in that bottle are 101 mg instead.

By using a scale only once, how can you immediately tell which bottle is bad?

(2) You have n bottles of pills.  Each bottle contains an unknown number of
pills.  The pills are supposed to be 100 mg, but some number of bottles
(maybe none of them, maybe all of them, maybe some number in between!) are
"bad": all the pills in those bottles (if any) are 101 mg instead.

By using a scale only once, how can you immediately tell which bottles, if
any, are bad?

Someone is going to object that the answer to the second problem is "not
realistic".  A good answer to this is probably to retort that it is not
realistic for a grown professional pharmacist to be playing number-theory
games in order to fix a dosimetry mistake, anyway. :-)

----- End forwarded message -----

-- 
Seth David Schoen <schoen at loyalty.org>  | And do not say, I will study when I
Temp.  http://www.loyalty.org/~schoen/  | have leisure; for perhaps you will
down:  http://www.loyalty.org/   (CAF)  | not have leisure.  -- Pirke Avot 2:5