§5 annex: More about sufficiency. This page elaborates on §5 of the home page.

§5X. The board-filling procedure starts with placing on the board any tile not all of whose hexagons lie in a straight line. Suitable are all the factory tiles, and tile 50 invented here as a minimal example:

figure 5a — tile 50

Now tiles are added:

figure 5b1 install tile 51 via 50a-50b	figure 5b2 install tile 52 via 50b-50c	figure 5b3 install tile 53 via 50c-51e
figure 5b4 install tile 54 via 52d-53d	figure 5b5 install tile 55 via 53e-54e	figure 5b6 install tile 56 via 54d-55d

At this point, the method should be clear. Here is the second time around the board:

figure 5c1 — add tile 57	figure 5c2 — add tile 58	figure 5c3 — add tile 59
figure 5c4 — add tile 5Z	figure 5c5 — add tile 5Y	figure 5c6 — add tile 5X

Third time around the board:

figure 5d1 — add tile 5W	figure 5d2 — add tile 5V	figure 5d3 — add tile 5U
figure 5d4 — add tile 5T	figure 5d5 — add tile 5S	figure 5d6 — add tile 5R

Very little of tile 5R, the final tile, is visible.

Now the board is full, and figure 5e merely unifies the colors:

figure 5e