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On 31 Oct 2006 21:50:30 -0800, "riverman" wrote:

No its not, its a matter of measurement precision.

No, it isn't. Or in the alternative, if it is, neither you or anyone
else could, as an absolute, measure whether C was farther than A or A
was farther than C. And if the latter is the case, your answer, above,
to your own question would still be incorrect.

Look, Myron, I'm not trying to bust your balls, and I'm not a
mathematician, so I've no idea as to what mathematicians consider
"oldies but goodies" or whatever when it comes to such problems,
puzzles, or whatever they call them. Maybe you forgot to give all the
details. But if you're now making/claiming assumptions you didn't state
originally, that's on you, and your answer as written to your own
question, also as written, is just wrong. Stated as you stated it, yes,
it is entirely possible for 2 (or 3 or 154 or "x") darts to be _exactly_
the same distance, especially in the theoretical "math puzzle" sense,
from a target.

Or, if one is going to operate in the completely practical sense and
take the position that even with the most accurate measuring devices
available, there's still no way to say "absolutely _exactly_ the same
distance," then it is equally impossible to state as an absolute that it
is always possible to determine which dart is further from the target.

Another alternative is that you are now assuming, but didn't then, or
did then and didn't disclose, that the darts are really "points," and
that in one axis, occupy a single, discreet plane. But that brings up a
host of problems for your answer, including the theoretical vs.
practical and/or the accuracy-of-measurement issue.



LOL. Certainly you're busting my balls. At least, I hope so, because
otherwise you sound like you're raving. The probability of two darts landing
a distance that is so close to identical from a target that it is beyond the
ability to be discerned is inversely proportional to the precision of the
measuring device. The more precise our devices, the less likely it is to
happen, and we have some phenominally precise devices, so the likihood of
this happening is relatively zero....that means its so close to zero that it
has no effect on the calculations.

Next, you'll assert that the odds of a coin landing Heads is not 50%,
because we forgot to count the times it lands on its edge. Or gets eaten by
a bird, or something. Those are relatively zero, although a coin landing on
edge is actually possible (I've had it happen twice in my life).

The point of this puzzler was to illustrate that how you approach the answer
is often the key to making something that seems unsolvable, solvable.

Here's a real oldie but goodie. You are racing a slow tortoise, and you give
the tortoise a head start. In the first moments, you run quickly to where
the tortoise started from, but in that time it has moved ahead. So you
continue to run to where it has advanced to....but it has moved ahead a bit
more. So you run to where it is AGAIN, but it has yet again moved ahead!
This proves that you cannot win the race, as you cannot catch the tortoise,
right?

:-)
--riverman