Working at the local pharmacy, you get a new shipment of Viagra pills
in 10 boxes. Each box contains 10,000 pills.
You open up the boxes, preparing to package the pills in separate bottles
when the Viagra supplier calls. "WAIT! Don't unpack the pills yet. We just
found out we had a packaging problem, and we know that in ONE of the boxes we sent
you, all of the pills were misweighed. We don't know which box it is,
but we do know that all normal pills will weigh exactly 100 mg while all
of the pills in the bad box weigh exactly 101 mg."
The shop is about to open, and ravenous customers are eager to get
their Viagra. It would be dangerous to give people overdosed pills
though. Who knows what kind of damage that could cause!
Luckily, next door is a hardware store which has a very precise
electronic scale, which can measure down to a single milligram. This is
the type of scale where you simply put something on top of it, activate it,
and it gives you a number, which is the precise weight of what's on it.
The scale is coin-operated and requires one quarter every time
you activate it.
You were hoping to save some arcade money for after work so,
what is the fewest times you need to use the electronic scale
to determine which is the box of defective pills (and how would you do it)?