We begin by defining the untangle as two strings lying vertical and not intersecting. We
assign the number 0 to this setting. Label each end of the strings as NE, NW, SE and
SW respectively. We have two operations that we can do on the tangle. Firstly, we can
switch the position of the SE and NE ends. This move is called twist. If we twist the
strings such that the gradient of the overstrand is positive, we call it the positive twist.
Otherwise, we call it the negative twist. When we carry out the twisting operation, we
add or subtract 1 from the tangle number, depending on the direction of twist