Carl is trying to find solutions to a geometric puzzle.

Riddle: Carl is trying to find solutions to a geometric puzzle. He has a square plot of land that he needs to reserve 1/4 for himself and divide the remaining 3/4 equally and in similar shape, among his 4 children. There are two possible solutions. Can you solve the puzzle?

Solution #1 – Squares
First, Carl divides his as to reserve to himself one-fourth in the form of a square.
Then, Carl takes the remaining 3/4 shape and scales it down by 1/4. He then, multiplies the shape into 4 identically shaped pieces, and aranges them so that they fit into the original 3/4 shape.
There is another solution too for this riddle!
First, Carl creates a triangle that is 1/4 the size of the square.

 

Then, with straight lines, he creates two squares. He proceeds to disect the two squares with horizontal lines creating 4 triangles. Then, he disects one of the resulting triangles from each square. The shape of land for each of his four children is divided evenly and is the same shape.

 

Solution #2 – Rectangles
First, create a triangle that is 1/4 the size of the square.
Now, with straight lines, create two squares.
Proceed to disect the two squares with horizontal lines creating 4 triangles.
Then, disect one of the resultuing triangles from each square. The shape of land for each of his four children is divided evenly and is the same shape.


Leave a Reply