Jumping frogs numbers game

This is the physical version of the puzzle described here : https://mathpickle.com/project/jumping-frogs/

Game rules

In the beginning of the game, there's one frog on each lilypad. The goal is to find a way for all the frogs to be together so they can all have a party.

The frogs are able to jump and stack themselves on top of other frogs, but they can only jump as many spaces as there are frogs in their current stack - that is, one frog by itself can jump one space, two frogs stacked together can jump two spaces, etc. 
They cannot jump on an empty lilypad, and all frogs from the same stack have to stay together.

In a modified version of the game, one of the frogs is a queen, and can only be at the top of a stack.

The game can be played with as many frogs (and corresponding lilypads) as you want, starting at three frogs for younger kids.

Please note that the attached picture is just for illustration purposes : as there are four lilypads on the base, only four of the frogs should be used to play the game. 

Physical version

Models included : 
- 3 different frog faces, 
- a model for eyes, to print in white (with a recess for the iris that should be easy to color with a marker)
- bases with different number of lilypads
- a crown for the queen

Each of these models (except the eyes) have holes for 10mm x 2mm magnets to be inserted during printing, which allow them to be stacked easily and securely.

Printing guidelines

The only thing to keep in mind is to add pauses when slicing the models so that the magnets can be inserted while printing (at two different heights for the frogs and at one height for the crown and lilypads). 

 

It's a good idea to mark the magnets poles beforehand (with a marker or stickers) so that they're all in the same orientation. You can also add a color change for the bases and print the bottom in blue and the lilypads themselves in green.

All models can be printed without supports. 

Source files

I've included the Fusion file as well so that you can add new faces for the frogs (each face is a configuration inside Fusion) and generate bases (the whole lilypad base is parametric so you should be able to change one single parameter and have Fusion regenerate the base for any number of lilypads).
I've also added other parameters (magnet height and diameter, easing, etc.) but do proceed with caution as they haven't been tested