2 Integer Partition (20 points)

For a given positive integer, we want to partition it into the sum of some positive integers, or itself. For example, 1 to 4 can be partitioned as

One way to partition 1.

Two ways to partition 2.

Four ways to partition 3.

Eight ways to partition 4.

If only 1, 2, or 3 can be used, there are only seven ways to parition 4.

A: How many ways to partition 5?

B: How many ways to partition 6?

C: How many ways to partition 7?

D: How many ways to partition 8?

2 Integer Partition (20 points) For a given positive integer, we want to partition it into the sum of some positive integers, or itself. For example, 1 to 4 can be partitioned as 21 + 1 3-1 11 =2+1 - 12 1 -3 1 . One way to partition 1 . Two ways to partition 2 . Four wavs to partition 3 . Eight ways to partition 4 If only 1, 2, or 3 can be used, there are only seven ways to parition 4 3-1 1 1 - 1 1+ 2 - 12+1 =2+2 =3+1 A: How many ways to partition 5? B: How many ways to partition 6? C:How many wavs to partition 7? D: How many ways to partition 8? 2 Integer Partition (20 points) For a given positive integer, we want to partition it into the sum of some positive integers, or itself. For example, 1 to 4 can be partitioned as 21 + 1 3-1 11 =2+1 - 12 1 -3 1 . One way to partition 1 . Two ways to partition 2 . Four wavs to partition 3 . Eight ways to partition 4 If only 1, 2, or 3 can be used, there are only seven ways to parition 4 3-1 1 1 - 1 1+ 2 - 12+1 =2+2 =3+1 A: How many ways to partition 5? B: How many ways to partition 6? C:How many wavs to partition 7? D: How many ways to partition 8