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[Phys-L] just for fun



On 12/18/2013 07:52 AM, Anthony Lapinski wrote:

which is bigger: 25/27 or 15/17?

Here's a mutation of that problem, not suitable for a placement
test, just for fun:

In your head, without a calculator, without even pencil and paper:

Which is bigger: 25/28 or 15/17?
^^

The method of solution is more interesting than the answer itself.

Hint: Key elements of one good method have already been mentioned
in the recent discussion.

This illustrates the point that there are /lots/ of ways of solving
any given problem, even a rather simple problem.

I use little puzzles like this to amuse myself when I'm stuck
waiting somewhere, and I'm not in the mood to think about anything
serious.

==============================================

Also:

You start out in the attic. There are three switches. It is known
that there are three light bulbs in the basement. The switches
control the lights, but you don't know which goes with which. You
get to make *one* trip to the basement to figure this out. How?

Some hints:

Whenever you get a question like this, the first step is to check
whether it is well posed. All too often, people skip this step.
The more time you spend working end-of-chapter problems the more
you devalue this step, because all too often such problems have
been crafted to be straightforward and well-posed.

Spoiler: The light/switch puzzle is grossly ill-posed.

New question: Prove scientifically that it is ill-posed, i.e. that
the original problem *cannot* be solved without making additional
assumptions.

Now for the creative part: Come up with an /interesting/ set of
assumptions that make the problem solvable.

Example: Here's a solution not involving much physics: Assume I
have a cell phone, and I have a friend with a cell phone. I send
the friend to the basement while I stay upstairs and flip switches.

This is not a joke; I've done exactly this on many many occasions,
when trying to find which circuit breaker controls which circuit.

So ... can you find some other set(s) of assumptions that lead to
a solution?

Huge hint: There are some that involve a bit of physics.

A discussion of how to deal with ill-posed problems can be found at
http://www.av8n.com/physics/ill-posed.htm