An odd thing happened last year during Oberlin's baseball season. Aaron had a higher batting average than Elijah did for the first half of the season, and he also had a higher batting average than Elijah did for the second half too. But Elijah had a higher batting average than Aaron for the season taken as a whole. Make up some figures to show how this could have happened.
(Recollection: We calculate a batting average by taking the number of times the batter is at bat and dividing it into the number of hits made. This is the fraction hits/at bats. The decimal is carried out to 3 places.)
(Note from Stella: This is all lies, of course. I haven't the faintest idea what happened to Oberlin's baseball team last year. But it makes an interesting problem and it can be solved.)
Solution
Here are some figures that work.
There are many possibilities.
It is interesting to explore whether Aaron must have more at bats than Elijah for this to work, and whether their half-season totals have to be so enormously different from each other.
