[math-fun] basketball shooting problem

This is a problem from the last Putnam exam that had me scribbling (which I don't have in front of me, but no matter) Say you're shooting baskets and you keep track of your record as you shoot them, for example 0 for 1 1 for 2 1 for 3 1 for 4 1 for 5 2 for 6 etc, you get the idea Someone specifies a "target ratio" (I think it was 80% in the problem statement) and you're told that during the record of shots, the shooter was below the target ratio, but later was better than the target ratio. Is there necessarily a moment at which the shooter must have shot exactly that ratio up to that point? Answer this for 80% and then generalize -- Thane Plambeck http://www.plambeck.org/ehome.htm