Problem set 1

I was just thinking about problem set 1. It looks like the first problem (unary digits of powers of 4) is a variation of the similar one for powers of 3 we did in class. Probably a similar approach will work. I think that the unary digits will always be 4 or 6, except for the case of 4^0, so I have to add 1 to the set as well. From there on, not too bad. since 4*4 ends in a 6 and 4*6 ends in a 4.

The second problem can be restated as an application of combinations of n objects taken 2 at a time. that would be (n!/(n-2)!)/2! which is of course n(n-1)/2 -- no proof required that way. Proving it by induction is an interesting problem. For the inductive step, I'll probably take the new element (the one that makes it n+1) and make tuples out of it and all the existing members. That plus the original tuples will probably do it.