DAY 281

SLY DOG

Credit: Solomon Golomb in the LA Times

There are four farmers named Able, Baker, Charlie, and Dog who live up a dirt road leading off the highway. They are located 1, 2, 3, and 4 miles, respectively, from the highway.

The county offers to pave the road up to Dog's place if the farmers will pay the cost of it, which the county reckons to to be $4800. So the boys get together at the local cafe where Dog proposes that they each pay a quarter of the cost. The others know that he's a sly old Dog, and they're skeptical. Abel, Baker, and Charlie never use the road to go beyond their own farms.

Is Dog's solution fair? Is there another way to distribute the cost that is more favorable to Abel, Baker, and Charlie, but is still fair?

Answer:

Think of the road as four sections, each one mile long, each costing $1200. Consider the road from the highway up to Abel. All four of them will use it, so they should each pay a quarter the cost of that mile, or $300 each. But the second mile is only used by Baker, Charlie, and Dog, so they should pay $400 each toward the second mile. Similarly, Charlie and Dog should pay $600 toward the third mile, and Dog should pay $1,200 for the last mile.

Thus Abel pays $300, Baker $700, Charlie $1,300, and Dog $2, 500.

NOTE: Not everyone would agree with this solution. In fact, Dog is threatening to pull out of the deal. He says he'll wait until the road gets to Charlie's, and then he'll only have to pay $1,200 for the last mile.