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From the book titled "Seminumerical Algorithms" second edition, by D. Knuth, page 363, exercice 4.5.3 number 39. says:

39. [M25] (R. W. Gosper) If a baseball player's battling average is .334, what is the fewest possible number of times he has been at bat?

!!! well how's about that! i'll make a guess that my pal from little league didn't know about that (nor did i). analysis is quite easy using the c.f. method i sketched. left as an exercise for math-funsters. was the c.f. method the intended approach? mike