I thought the recent baseball puzzler was pretty good. I was puzzled for a while, but then I thought "hey, if the first half batting avg was .25 and the second half was .375, about the only thing you can say is that the entire season’s batting average was something in-between .25 and .375. " Without knowing how many at bats in each half, you can’t say more than that. So my mind finally un-puzzled, I was able to figure it out.
In Ray and Tom’s example, the number of at bats was in the hundreds. And some of the segment at-bats were half-at-bats; i.e. not integers. But an integer number of at bats would be necessary for actual baseball players.
Ok, try this for extra credit: What is the minimum number of at-bats consistent with the puzzler? Include the restriction that the number of at-bats in each segment by both players are all integers.
Remember, both players had the same total at bats for the seaon.