Tower of Hanoi

What I've learned, thus far, about the Tower of Hanoi is that it is all about observeable patterns. Firstly, when you start out with an odd number of pieces, it is most effiecient if your first move is to place the top piece on the farthest peg. However, when you have an even number of pieces it is best to move the first piece to the center peg. Secondly, and probably most important, is the pattern that is visible if you make the following chart.

piece(s) | move(s)
_________________
1 | 1
2 | 3
3 | 7
4 | 15
5 | 31
6 | 63

From this pattern one may infer that the formula 2*-1, where * is equal to the number of pieces, will give the number of moves necessary to complete the puzzle.

Serially Interlocking [4 piece puzzle]

Just so there is no confusion: a - is red, b - is white, c - is silver, d - is black. The order the connect in is red and black, next silver, lastly white. My puzzle didn't successfully interlock, but that was due to the cubes needing more sanding than I had planned on.
This puzzle took some imagination. I first set to finding the possible ways in which the a and b could interlock, being that these both had two sets of 3 connected cubes. Once I tested out the possibilities, it became clear that there was really only one possibility. Then I had to figure out which sequence to put the pieces together in.
And so it goes from left to right: a (left side facing down, right side facing up), connecting with d (upside down), connecting with c (upside down), and b (looking like an inverted capital J).

SOMA: Deficient Pieces

I used a different color of swirl on each piece to indicate their placement in the photos. Although they are put together differently the first two SOMA cubes have the same deficient piece (the piece marked with white swirls).

The third cube has a different deficient piece (the piece marked with silver swirls). This piece is both deficient and central.

Topological Equivalency [converting C-G]

Okay, so I'm not an artist. I had to make multiple copies and use white out, and trace parts. This was a nice topological puzzle. It took some thought, but it wasn't terribly difficult.
I can now say that topology is fun, whereas before I thought it futile.

Yet more topology

Once again - a topological puzzle. This puzzle is in some respects is similar to Reefer Madness. I must admit I had help with this puzzle.

Had I not asked a classmate for some assistance I'd have never completed it, because I thought that our assignment was to remove the string from the center hole, allowing the two beads to be on one line. I tried different techniques,

and thought really hard, and then came to the conclusion that it was impossible. I was right. It was impossible. It was also not the assignment at all.