-----Original Message----- From: math-fun-bounces+andy.latto=pobox.com@mailman.xmission.com [mailto:math-fun-bounces+andy.latto=pobox.com@mailman.xmission.com]On Behalf Of dasimov@earthlink.net Sent: Tuesday, October 25, 2005 9:49 PM To: math-fun Subject: RE: [math-fun] basketball shooting problem
Andy wrote, in conclusion:
<< So it is impossible to cross the target without hitting it if the target for hits/misses is an integer K, or equivalently, if (hits/(hits + misses)) is of the form K/K+1 for some integer K.
Aha -- so by symmetry of hits <--> misses, this also implies the impossibility of jumping over the target if it's of the form 1/(K+1).
Careful! You have to reverse "above" and "below" when you exploit the symmetry. You can jump from below 1/(K+1) to above 1/(K+1), but you can't jump from above the target to below it without hitting it exactly if it's of the form 1/(K+1). For targets of the form K/(K+1), you can jump from above to below without hitting the target exactly, but must hit the target going from below to above. And those are the only "mandatory target hit" numbers. Andy Latto andy.latto@pobox.com