#2             71. A HOLE IN ONE                       
Miriam removed her foot gingerly from the hole in the floor. It looked as though some time in the past the white ants had had a good feed, and for some perverse reason the timber had now just given way.

“We shall have to replace this whole section,” said Audrey, indicating a rectangle 40 cm long and 15 cm wide.

“I think I have a suitable piece of wood in the garage.”

She soon returned with a board 60 cm long and 10 cm wide.

“That will never fit!” exclaimed Miriam.

“Sure it will,” replied Audrey, “as soon as figure out how I’m going to saw it in two!”

Amazingly enough, the board did fit the hole, and it was cut into only two pieces.

How was it done?
HINT 1

Measure the areas of the hole and the board. Is a solution to the problem possible?
HINT 2

If there is a solution, the board will have to be cut in some way which matches the dimensions of the hole.
SOLUTION

The cross-cuts in the board are a third the way along, and the horizontal cut half way. The right-hand part of the cut board is translated up and left to complete the repair.
EXTENSIONS

1. Put yourself in Audrey’s place. How do you actually make this cut using a handsaw? You may have a problem!

2. This problem can be thought of as a plane tessellation problem (in some disguise). The two pieces that the board is cut into are congruent, and form part of a tessellation of the plane. There are many problems involving plane tessellations. Look up ‘tessellation’ on the internet.