Problem #7: Arithmagons

The idea of a secret number on the points and the sum of those numbers on the side stumped me for a second. For some reason I kept thinking of the sum as the length of the sides and the secret number as some sort of angle. I was trying to incorporate geometry where I only needed a little algebra. Once I wrapped my mind around what I was doing, I started making equations and manipulating them. I eventually could prove that the magic numbers were 1, 10 and 17.

I generalized this with more letters and got the secret numbers (A, B & C) in terms of the sides (x, y & z). My brain works much better with manipulation, variables and algebra. I could make these statements, prove it with some numbers and I would be satisfied with this.

My boyfriend actually walked by and took a look at it, when I explained it with numbers he was so confused. This led me to my written work, justifying the equations I had previously come up with.

I was even more satisfied with this answer. Again, my brain was ready to just accept the equations, simply because I believed in my own mathematical ability. Once I actually explained it, the equations were completely correct and I could justify them.

Next I tried to move on to one of the more complicated shapes given in the problem set. I made variables and equations and tried to go about manipulating like I did the first time.

I figured I would focus on one shape at a time. The first one I tried to tackle was the parallelogram shaped-thing on the top right. I couldn't do anything with the equations! Every time I subbed something in it ended in a roundabout where the magic number part would algebraically disappear. I plan on giving this some time and revisiting. Any one else have some thoughts on how to start?