I came across an interesting question:

How many ways you can split 20 into? For example, {20} as a single group is one way, {1,1,...1} as 1s in 20 groups is another way. And many other ways in middle such as {18,1,1}, {4,4,4,4}, et al. In total, how many such ways.

And another question on top of the above, how many such ways contain at least one group with number greater or equal to 5? For example, {17,3} is one such way because 17 >= 5. {6,6,8} is another way because 6 >= 5 and 8 >= 5. {3,3,3,3,3,3,2} isn't such a way because 3 and 2 both < 5.