Final Project

Moving only three matchsticks, make the matches spell a word.


for the solution go to: http://amanda-finalproject.blogspot.com/

Rubik's Cube

I couldn't solve the Rubik's cube. Even with directions, I just couldn't do it. I do know that the Rubik's cube is considered group theory, because a single move in actuality involves multiple pieces moving at once. This is probably why I had so much trouble with it.

Peg Solitaire

Working with peg solitaire (the English cross) proved to be interesting because of the various patterns involved in solving the larger cross. I found it most effective to move from the corners toward the center. I really enjoyed this puzzle.

Mini Ma's

The minimum number of moves for the puzzle on the webpage is 28. I was baffled as to how to solve this one. I used Sarah's solution to get through it.

Curses, coiled again!

The only difference in solving the puzzles which are coiled in different directions is that the string must be wound in a different direction.

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.

Activity 11 - Puzzle K

I found this puzzle to be a little less challenging than the previous topological puzzles we've worked on. There were two reasons for this: I now have some understanding of how topology works, and I saw one of my classmates trying to work out the solution from a distance. Seeing the puzzle from a distance made it easier for me to work out in my mind.

Reefer Madness

This is a topological puzzle where in order to solve it the "knot" must be brought to the opposite side of the small loop to be undone.

It took me quite a while to solve this one, that is I was able to untie it, but was very confused when it came time to work it back into its original state. I ended up having to work backwards step by step.

Instant Insanity

Pt. 2

This is where I started. I then decided to flip the cubes over to see what I had to work with on the reverse side.

At this point I knew that the cubes with double blue and double green might present a problem. I played with them for a while and thought about it. I figured that I should focus on the blue and the green would naturally fall into place.

I had to make sure that all the blue faces were set to different sides of the sequence. Leaving the double blue in place I mainpulated cubes 1 and 3 - 4 not having a blue face.

Now that all the blue faces were on different sides the only piece left to play out was cube 4. Realizing that the other greens were on the still viewable sides, I just flipped cube 4 until the greens were on the unviewable side.

Voila!

Instant Insanity

Pt. 1

So the easiest way to solve the puzzle would be to set each cube in such a way that each color was displayed on one side. Cube 2 makes this an impossibility. So one must find a way around this small obstacle.

I began by eliminating all the extra sides (a.k.a. faces). I figured in order to solve the puzzle there should be four faces of each color in play/motion. That meant that 1 blue, 2 yellow, 2 green, and 3 reds should be out of motion.

I decided to line up the yellows, which inadvertantly aligned the reds, which gave me few options. I decided to eliminate the 2 reds opposite eachother on block 1, the 2 greens opposite eachother on block 2, the yellow/green on block 3,

and yellow/red on block 4. Now that the excess was eliminated I could work much more easily.