dan asimov:

Michael Reed wrote:

who??

<< . . .when i was a (younger!) kid in little league baseball, one of my friends told me that he had calculated his batting average . . . and that it was .399 . immediately i knew that this could not be correct. how did i know?

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I'm gonna guess that if |2/5 - p/q| < 1/1000 then q must be greater than any reasonable number of at-bats in one Little League season.

this is essentially it, although the inequality should be .5 / 1000 < 2/5 - p/q < 1.5 / 1000 . fwiw, i remember wondering at the time if it was possible that my friend's calculator read ".39999999" and they truncated instead of rounding. this doesn't seem a reasonable explanation.

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.

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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).

--Dan

it depends which direction one jumps over the target, see my earlier message. before-above and after-below requires one hits the target. before-below and after-above does not. mike