So here is my second attempt at **Puzzle 68** (with \$$x \leq y\$$ to mean given y, we can get x):

Define \$$(a', b', c') \leq (a, b, c)\$$ when

1. If \$$\frac{a}{2}=b\$$ then \$$a'=0,\,b'=0,\,c'=c+b\$$

2. If \$$\frac{a}{2}\lt b\$$ then \$$a'=0,\,b'=b-\frac{a}{2},\,c'=c+\frac{a}{2}\$$

3. If \$$\frac{a}{2}\gt b\$$ then \$$a'=a-2b,\,b'=0,\,c'=c+b\$$

4. If \$$a=0\,or\,b=0\$$ then \$$a'=a,\,b'=b,\,c'=c\$$

Side question : does anybody know how to make a big curly left bracket with 4 rows and 1 column? I tried

/left/{/begin{matrix}a//b//c/end{matrix}/right. (i switched \ with / because it keeps trying to read it as a code.)

but doesn't seem to work.