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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?
Answer: 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. 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.
Solution:
Show Answer
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.
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.
Show Answer
Solution #1 – Squares
First, Carl divides his as to reserve to himself one-fourth in the form of a square.
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.
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.
A man is walking down a road with a basket of eggs. As he is walking he meets someone who buys one-half of his eggs plus one-half of an egg. He walks a little further and meets another person who buys one-half of his eggs plus one-half of an egg. After proceeding further he meets another person who buys one-half of his eggs plus one half an egg. At this point he has sold all of his eggs, and he never broke an egg. How many eggs did the man have to start with?
Answer: 7 eggs. The first person bought one half of his eggs plus one half an egg (3 1/2 + 1/2 = 4 eggs) This left him 3 eggs. The second person bought one-half of his eggs plus one half an egg, (1 1/2 + 1/2 = 2 eggs) leaving the man 1 egg. The last person bought one-half of his eggs plus one-half an egg, (1/2 + 1/2 = 1 egg) leaving no eggs.
Solution:
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7 eggs. The first person bought one half of his eggs plus one half an egg (3 1/2 + 1/2 = 4 eggs) This left him 3 eggs. The second person bought one-half of his eggs plus one half an egg, (1 1/2 + 1/2 = 2 eggs) leaving the man 1 egg. The last person bought one-half of his eggs plus one-half an egg, (1/2 + 1/2 = 1 egg) leaving no eggs.
Show Answer
7 eggs. The first person bought one half of his eggs plus one half an egg (3 1/2 + 1/2 = 4 eggs) This left him 3 eggs. The second person bought one-half of his eggs plus one half an egg, (1 1/2 + 1/2 = 2 eggs) leaving the man 1 egg. The last person bought one-half of his eggs plus one-half an egg, (1/2 + 1/2 = 1 egg) leaving no eggs.
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