Notes on the Radix Puzzle

How to solve the radix, as shown to me by Devin F., August 29, 2011.

The basic idea is that untangling the two hooks is a puzzle in itself (albeit a
rather easy one), even without the shoe. The key is to position the shoe so the
hooks can go through the same motion that they would if it wasn't there.

First I will introduce some names for the pieces and their features.

Hook. Large piece of brass. There are two of these.
Foot. The flat end of the straight part of the hook.
Shoe. The small piece with two holes.
Large/Small hole. The shoe's larger/smaller hole in the shoe. If the shoe is
  oriented so that the "Hanayama" logo is readable as ordinary english text, the
  large hole is on the right.
Bottom of the shoe. The flat side with the "Hanayama" logo.
Tip. The end of the curled part of the hook.
Large/Small hump. The two bumps on the edge of the shoe, next to the large/small hole.
Large/Small notch. The notch are indentations on the curled part of large/small hook.
Large/Small foot. The larger/smaller of the two feet.
Large/Small hook. The hook with the large/small foot.
Large/Small tip. The tip of the large/small hook. (Both tips are actually about
  the same size)

1. INITIAL STATE
All three pieces are entangled, and the feet are in the shoes. The large hole
is on the large foot, but the small hook is free (it is sitting in the shoe but
it can be removed). The bottom of the large foot is flat against the bottom of
the large hole, and similarly for the bottom of the small foot. The bottom of
the shoe is facing down. The large hump is facing you. The puzzle can stand on
a table in this configuration.  To untangle the hooks, raise the shoe to the
middle of the arc of the large hook, and thread the small tip through the top
of the small hole and keep going as far as you can.  Orient the large hook so
that the notch and the radix logo on the foot are facing up, and the end of the
large foot is facing right. You want to achieve a state in which the large
notch, the small foot, the small hump, the large tip (end pointing up), the
small tip (end pointing away from you, horizontally), and the large foot are in
a straight line, in that order. *** This is the most difficult step, you just
have to fiddle with it for a while.*** At this point you can slide the shoe
down to the large foot while leaving everything else in place and the two hooks
will be untangled.

2. UNTANGLED BUT CONNECTED STATE
The large foot is in the large hole just as in the initial state, but now the
two hooks are not entangled, and the small foot is in the small hole, but
upside down (the end is poking out the top of the foot). Both tips are pointing
up. At this point you want to thread the small hook off the shoe. Orient the
large hook and shoe as in the initial state. Thread the small hook off until it
is almost off, and the small tip is pointing up and is near the end of the
large foot. Continue to thread while twisting the small hook so that it is
almost out, with the tip pointing down in the small hole. Then lift the tip out
and swing the arc of the hook around the bottom of the shoe to remove the small
hook entirely. It slides off in a "d" orientation, to the right, with the tip
facing right.

3. UNTANGLED WITH THE SHOE ON THE LARGE HOOK
Here the small hook is completely free, and the shoe is on the large foot as in
the initial state. Remove the shoe by sliding it to the large notch, rotating
it 180 degrees, and then removing it off the large tip.

4. COMPLETELY SEPARATED
All three pieces are completely separated.

To re-assemble, follow the above steps in reverse.