Five of Eternity II's 22 colors appear only along the border ring, each on exactly 24 edges, never once in the interior. A structural split that shapes how every solver treats the frame.
findingFindingmeasurementprovenWhy it resistsUpdated 2026-07-01
Reproducedeterministic — reproduces byte-for-byte·reruns the search
The 22 colors don't play equal roles. Sort them by where their edges sit and
they split into two clean classes: five rare colors fenced off to the border,
and seventeen common colors that do almost all their work inside the board.
Pick one of the five rare colors and watch the board: all 24 of its edges light
up around the frame ring, and the 14×14 interior stays completely blank. Switch
to a common color and the interior fills instead. That empty middle, for every
rare color, is the whole finding.
Rare colours (border-only) — pick one:
vs a common one:
Colour 1rare
on the frame ring
24
in the interior
0
total edges
24
Every one of this colour's edges sits on the frame ring. Not a single one appears in the 14×14 interior — that empty middle is the whole finding.
The board map of a single color's edges. Rare colors are pure frame (0 interior); common colors are the mirror image. Counts are exact, from the official piece set.
The split itself is structural, not a defensive trick. Because the outer rim
is solid grey, every border piece keeps its grey edge facing out, so its
coloured edges only ever meet other border edges or the interior: the border
and interior colours live in separate pools no matter what. The five border
colours read as "rare" simply because there are far fewer border edges to
colour, and they could be relabelled to any five values (even reusing interior
ones) without changing the puzzle at all. (See the design note on
why, with thanks to Vasily V.
on the groups.io list for the correction.)
What is real, and what matters for solving, is the consequence: the 14×14
interior is left to seventeen common colours with no rare, highly-constraining
signal anywhere in it, which is a large part of why interior search has so
little to grip. The border, where the colour pool is small and matches are
tight, is correspondingly the part every strong board gets essentially perfect.
Eternity II's colour counts were balanced to remove the statistical handholds
that sank Eternity I; this geography is where you feel the result.