The Missing Block
I found this problem in a puzzle book titled "The Ultimate
Clever Puzzle Book". I was so intrigued by this that I decided
to investigate what underlies the mystery and recruited Matt and
BJ to help me figure it out.
The problem goes as such:
Start with an 8 unit by 8 unit square
Count the number of blocks that make up this pattern to find
the the area; the area of this square is 64 units
Now, cut along the two black lines and the one blue line in
the picture below
You have two congruent triangles and two congruent trapezoids
The objective now is to rearrange these four pieces into a
rectangle, which should look line the one below
Now, how many blocks are there?
The new figure is thirteen blocks long and five blocks high
which gives us sixty five blocks. Where did the extra block come
from?