Theory

Every record board we have is frozen in place. You cannot nudge your way from a great board to a perfect one, and we can prove it.

If you can't improve a great board by polishing it, maybe you can jump to a different great board. On every record pair tested, you can't, and the structural reason why is worth seeing.

Almost every small patch of pieces you could build is impossible. For a 2×2 square, 99.72% of the ways to place four pieces can never be made to match.

A solved board hides a simple bookkeeping law: every colour the border hands to the interior, the interior hands straight back. Break it and you know instantly the board is wrong; obeying it, though, guarantees nothing.

Eternity II has two rules: edges must match, and each piece is used once. The first is generous. All the hardness lives in the second.