1. The Farmer and the Visitor
A farmer felt insulted when a snobby visitor from another town criticized his barn.
“What’s wrong with my barn?” the farmer asked.
“It’s too small,” the snobby visitor sniffed. “And the floor is made of dirt. Back home, our barn floors are made of smooth concrete. They’re so clean you can eat off them.”
The farmer decided he could do nothing to increase the size of his barn. But he could improve the quality of the barn floor. First he had it cemented over. But that wasn’t good enough. He needed something to put over the floor.

2. “How about hay?” the salesperson at the store suggested.
“Hay is nice for a barn floor.”
“Not good enough,” the farmer said.
The salesperson brought out other coverings for the barn floor, each one more expensive than the last. To each, the farmer had the same response:
“Not good enough.”
Finally, the salesperson brought in a sample of beautiful royal blue carpeting.
“Now that’s what I call good enough,” the farmer said.

3. The carpeting came in squares of various sizes
The carpeting came in squares of various sizes. The barn floor measured 36 meters by 18 meters and the farmer wanted all the carpeting to fit perfectly. He could not bear to make even one cut through such beautiful carpeting.
36m
18m

4. 2. How large would the squares be?
1. If all of the squares are the same size, what is the least number of squares the farmer can use to cover the floor?
2. How large would the squares be?
18m
18m
18m
18m
36m
18m
12m
12m
12m
12m
12m
12m
12m
10m
10m
10m
10m
10m
10m
10m
10m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m

5. 4. How many of each type should he order?
3. If the farmer covers the floor with two different sized squares, what should their dimensions be?
4. How many of each type should he order?
18m
18m
18m
18m
36m
18m
12m
12m
12m
12m
12m
12m
12m
10m
10m
10m
10m
10m
10m
10m
10m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 8m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 6m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 4m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m 2m