Rough week gone by, so many assignments due in this one week. Finishing problem set #5 was straight forward, but going into the weekend A2 would give me and my partner quite a bit of trouble. Questions 2, 3 and 4 were fairly straight forward and didn't take too much time to tackle them.

Question 1 was another story, we spent most of our time on the ternary tree question as we couldn't find a suitable pattern or closed form to describe the relationship between the number of nodes and the number of non equivalent ternary trees. We had gone through many ways of counting the number of ternary trees including the grueling task of drawing out all of the possible ternary trees for nodes 1 to 4 and still to no avail, we couldn't pin down a closed form. Many of our findings hinted to a possible closed form where some numbers were repeated from the previous number of nodes, but there always seemed to be some constant that would hang around and we couldn't find a pattern that would derive these.

To solve this seemingly impossible question we took advantage of Danny's office hours and we asked him how we should go about finding the closed form. After showing him our pages of rough work he worked with us and helped us find a way to count the trees by grouping all the ternary trees the right side of the tree could make with the left side having 0 nodes, then having 1 node, and so on. This was really helpful and we returned home to take another crack at the question. We had it pretty much figured out but the deadline drew near and we were not able to piece together a full solution before handing it in. We managed to summarize how we would go about proving the formula but hopefully next time we won't get such a tough question.

Test #2 is next, lets hope for the best, good luck.