Riddle of the Week

Riddle of the Week: Getting the Goat

Difficulty level: Moderate

Michael Stillwell
 
By Jay Bennett

Welcome back to Popular Mechanics' Riddle of the Week! This week we take a look at a math riddle found in L.H. Longley-Cook's book Work This One Out: 105 Puzzling Brain-Teasers. A scholar of credibility theory, or the use of recent past events to change statistical predictions of future events, Longley-Cook also enjoyed penning math puzzles. This one is about two brothers who decide to divvy up the family dairy farm.

PROBLEM

Two brothers each have an equal stake in a dairy farm, but after the price of milk drops, they decide to go their separate ways and start raising lambs instead. The brothers sell off their cows, and sell each cow for as many dollars as they have cows. They use that money to buy lambs for $10 apiece. Once they have purchased as many lambs as they can with the money from the cow sales, they have a little left over, which they use to buy a kid goat.

The two brothers now have purchased an even number of animals. They split the animals evenly, but the brother who gets the goat wants a sum of money from the brother who gets all lambs to equalize the value.

How much money should the brother with the goat receive?

HINT

With math riddles like these, it is often best to start plugging in numbers and see what you get. Choose a number for the cows that the brothers have at the beginning and see if the rest of the parameters for the riddle can be satisfied. After a bit of trial and error, a pattern should emerge.

SOLUTION

Once you settle this financial dispute between the two livestock-raising brothers, you can check back for the solution on Friday.