Al, Bert, and Carl are on a road trip, and stop at a roadside picnic table for lunch. Al has five sandwiches. Bert has three sandwiches. Carl, who is a little absent-minded, realizes that he forgot to stop at the Deli that morning. He has the $8 that he was going to buy his sandwiches with and offers it to Al and Bert for some of their lunch.
It is decided that the three of them will divide the 8 sandwiches equally, and then Al and Bert will divide the $8. After lunch, Bert picks up four of the dollars. but Al says that it is not fair. He says he should have more. Carl agrees that All should have nore. He says that since Al contributed 5 of the sandwiches and Bert contributed 3, Al should get $5 and Bert should get $3
Is this the most fair division of the money?
(The site I found this on calls it a "classic" puzzle, but does not give any other information about its source.)
(In reply to Problem Solution
by K Sengupta)
By the problem, number of sandwiches consumed by each of the men is 8/3
Bert contributed 3 sandwiches, and thus gave only 3 -8/3 = 1/3 sandwiches for Carl to consume, while Al brought 5 sandwiches, and so he gave 5 - 8/3 = 7/3 sandwiches to Carl.
Thus, the sandwiches given respectively by Al and Bert to Carl are in the ratio of 7:1, and accordingly the $8 received as payment should be divided in the same ratio.
Thus, Al should get $7 while Bert should receive $1.
Edited on July 30, 2012, 3:23 am