## ________________

Business decisions often require problem solving, as the coach points out with these puzzles.

## ________________

### Pondering Productivity

Smith and Jones each manage egg farms.
Smith says: “1 1/7 of my hens lay 1 1/6 eggs in 1 1/5 days.”
Jones says: “1 1/5 of my hens lay 1 1/6 eggs in 1 1/7 days.”

(a) Is either farm more productive than the other in eggs per hen per day?
(b) Smith has 48 hens. How long must he wait to first get a whole number of eggs at the close of a day? How many eggs does his farm produce in that time?
(c) Jones has 300 hens. How many days must he wait to first get a whole number of eggs at the close of a day? How many eggs does his farm produce in that time?

### Cornfield Planning

A farmer has a square plot of land that measures 100 feet on each side. She plans to grow corn in the plot, and she will install a fence around the corn. Fencing is expensive, so she wants to grow the corn in a shape that will maximize the ratio of the area of the cornfield to its perimeter.

What shape should the cornfield be?

## Solutions to week 138

In Close to a Quart, the minimum number of transfers is 210. For Math Party, the children are 4, 4, and 9.

Close to a Quart answer explained:
By transferring water n = 2(a + b – 1) times, you can achieve water in one of the two containers in the amount of ae – bπ or aπ – be, making sure the expression used is positive. You must find the smallest integer value of a + b so that
.99 < ae – bπ < 1.01 or .99 < aπ - be < 1.01. By numerical search, you find 73π - 84e = 1.00059 and 57e – 49π = 1.004024 are the smallest values satisfying the above conditions. Thus a = 57 and b = 49 gives n = 210 as the minimum number of transfers.