Mandatory assignment solutions

Here are our suggested solutions to the mandatory assignment. Please let me know is something is unclear or (!) wrong.

For some of the problems there are alternative solutions. Some of these are more elegant than what we have suggested.

Two small comments:

• In Problem 1 (e) we expected you to prove by combinatorial reasoning that there are 52 partitions of Z and not simply refer to the OEIS. We took points away if you omitted this, but only if you were still passing the assignment.
• Problem 2 (a) was slightly more finicky than we expected, but the technical details are not insurmountable.

I am generally impressed with what many of you have performed.

Ole