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On 12/31/2014 06:54 PM, I wrote:
consider the following transmogrificationHere is one possible answer: In a certain factory,
of the original question:
It takes 5 minutes for 5 machines to make 5 widgets.
So, how many machines does it take to make 100
widgets in 100 minutes?
it takes only *one* such machine to turn out 100
widgets in 100 minutes.
Spoiler: Here's how it works, in this particular
factory: The machine takes four minutes and 2.5
seconds to warm up. Thereafter it can bang out a
new widget every 57.5 seconds. That means the first
widget appears at the 5 minute mark exactly, in
accordance with the statement of the problem. It
can bang out 99 more in the remaining 95 minutes,
with a few seconds left over.
This is not a contrived or unphysical possibility.
Things like this happen in the real world all the
time. In addition to "warmup" issues, there are
also "pipeline" issues. A garden hose can put out
a ml of water in a few milliseconds. However, that
does not mean that any particular ml made it all the
way from the well to the outlet in a few milliseconds,
or even a few seconds. It spent a long time in the
pipeline. Similarly, if you buy a desktop rated at
10,000 bogomips, that does not mean that it can carry
out one instruction -- from start to finish -- in 0.1
ns or even 1 ns. There is a lot of pipelining.
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