A farmer passes on, leaving his herd of 11 dairy cows to his three sons.
His will says:
The oldest son gets 1/2 of the herd.
The second son gets 1/4 of the herd.
The youngest son gets 1/6 of the herd.
The sons mourn the passing of their father, but they're pleased that each
of them will have a (small) herd of cows... until they realize that 11
can't be divided by 2, 4, or 6. Following the will would result in
cutting up cows into halves, fourths, or even sixths. Ick!
Just then a wandering mathematician rides up on a cow. The brothers tell
her about their problem, and she says, "Never fear -- I can help!" She
dismounts, and gives her cow to the brothers, so that they have a total of
11 + 1 = 12 cows. Then they divide the cows according to the will:
The oldest son gets 1/2 of 12, or 6 cows.
The second son gets 1/4 of 12, or 3 cows.
The youngest son gets 1/6 of 12, or 2 cows.
But wait -- 6 + 3 + 2 = 11, so the three sons together have 11 cows total.
This leaves one cow left over. So the mathematician takes her original
cow and rides off into the sunset, leaving the brothers stunned at the
brilliance of her solution.
So here's the question: did each brother get a fair share, or did somebody
get ripped off? I'll give a couple of extra points on the next quiz to
people who write down a reasonable answer and explanation, and give it to
me in class on Wednesday, March 12th.