Paying for Rotation: Zig-Zig Case

Always a spare gold coin ``liberated''...

Claim: Either or .

This is implied by the fact that either or .

Proof by contradiction: If not, then

• and .
• So .
• This implies |A|+|B|+1+|C|+|D|+1 > |A|+|B|+|C|+|D|+3.
• That is: 2>3... contradiction.

Zig-zag case a little different, but same result.