Learn how a new piece moves, then plan a route that collects every gem.
The full guide, with a worked example and common mistakes: How to play Movement Patterns.
Eleven: frog, robot, rocket, kangaroo, octopus, bee, crab, ladybird, ghost, UFO and chameleon.
Some can only ever reach part of the board (a frog, a bee), and some can't go down. Tours are offered with the robot and ladybird, which can reach every square.
Only a little — the knight on Knight's Tour is one such piece. These pieces are all invented.