Malik’s little brother is building towers with a set of unit blocks, which are blocks of length 1 inch, 2 inches, 3 inches and so on. The diagram at the right shows a few of the ways to make a 4 inch tower.
How many ways are there to make towers of the following heights: 1,2,3,4,5, and 6 inches? Remember that you can use as many blocks as you need, of any whole-number length. Organize your work so that you can find patterns.
Based on the pattern you found, how many ways are there to make a tower 12 inches high? Explain how you got your answer.
Malik has decided to share his blocks with you, but has only given you 1 inch and 2-inch blocks. Using only these blocks, how many ways are there to make towers of each height up to 6 inches? Can you answer this with your work from part (a)? Look for a new pattern.
Describe the new pattern you found, and use it to describe the number of ways there are to make every height up to 20 inches. Do you know the name for these numbers? Explain why this pattern makes sense.
-----------------
PLs HELP!! you will get 100 points!!