The numbers every Eternity II researcher ends up re-deriving, collected in one place with their provenance: the puzzle definition, the clue placements, scoring conventions, the record table, search-space sizes and the structural counts.
Every conversation about Eternity II eventually stops while someone re-derives
the same handful of numbers. This page is that handful, written down once.
Facts marked computed are re-derived exactly from the official piece set,
the same data our reference numbers and
Why is it hard? pages are checked against, and anyone can
reproduce them. Record facts come from the primary mailing-list messages;
encyclopedic facts from Wikipedia.
The grey outer-border colour is not one of the 22: it never appears on an
internal edge. The 5 + 17 colour split is not an accident: 17 interior
colours is exactly the hardness peak for a
puzzle of this size.
The rules sheet pins one piece; Tomy sold four smaller
clue puzzles whose
solutions each revealed one more placement, and the remaining placements were
published later. Squares use the board notation of
e2.bucas.name: rows A–P from the top, columns 1–16
from the left. Piece numbers are 1–256 in the official list order, and the
rotation is clockwise from the piece's stored orientation.
Square
Piece
Rotation
Which clue
I8
139
0°
mandatory (in the rulebook)
C3
208
90°
clue puzzle
C14
255
90°
clue puzzle
N3
181
90°
clue puzzle
N14
249
180°
clue puzzle
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The five fixed clue placements, to scale on the board.
A board that respects all five is called strict-canonical; most record
boards respect only the mandatory centre clue ("canonical"). That distinction
splits the record table in two; see below.
The clues also settle a counting question: with only the mandatory piece
placed, complex theory expects ≈ 14,702 full
solutions; with all five, ≈ 1. The 5-clue puzzle has, by design, a single
expected solution.
Score = matched internal edges, out of 480. The 60 outward-facing grey
edges around the frame are not counted. This is the convention of the prize
scrutiny, of every record in the table below, and of this wiki.
"Breaks" = 480 − score. Solver authors often report mismatch counts
instead: Blackwood's 468 was announced to the mailing list as "12 breaks".
479 is possible, but only through the border. A launch-summer
parity argument claimed exactly
one mismatch cannot exist
(kubzpa, 2007), and it holds
for interior moves (rotating an interior piece with equal opposite edges
breaks two, giving 478,
msg 1642). But the parity
leaks through the 60 unscored outward border edges: flip a border piece
whose two ring-facing sides share a colour and exactly one scored edge
breaks (Verhaard, 2009).
The official set has 14 such border pieces (computed), so any full
solution implies a 479.
Check the piece set before comparing scores. Several headline "480"
boards use variant piece sets (Clue-1/Clue-2
designs, mixed sets, the unframed TopCoder variant). They are different
puzzles; see Records & solvers.
The 480 internal edges split into three families (computed):
The full timeline, with board previews and per-record references, lives at
Records & solvers. The numbers themselves:
Score
Who
When
Track
467
Louis Verhaard's team
Sept 2008
canonical; won the $10,000 partial prize
468
Joshua Blackwood
Aug 2020
canonical
469
Peter McGavin (Blackwood's solver)
Sept 2020
canonical
469
various (~7 boards, independent finds plus one single-swap of McGavin's)
Nov 2020
canonical
470
Joshua Blackwood
Mar 2021
canonical, the ceiling since
470
Jef Bucas
Dec 2024
canonical (tie of the 470)
460
Bruno Gauthier
Mar 2023
strict-canonical; best board respecting the four optional clues, 2023 until beaten Jul 2026
464
Benjamin Riotte
Jul 2026
strict-canonical record; beat Gauthier's 460, all five clues respected
"480"
various
2023
variant piece sets, not the canonical puzzle
The 469s were long quoted as the ceiling, but board-level verification shows
the 468/469/470 boards are all the same starter-only regime (the contest
rules pinned only the starter piece), so the 470 is the record on the same
puzzle, not an easier variant. A full canonical solution (480/480) has never
been reported by anyone, in any public source. The gap of 10 edges has stood
since March 2021.
The 10⁵⁵⁷ figure is worth being able to re-derive rather than cite: the 4
corner pieces go to the 4 corners (orientation forced by the two grey sides),
the 56 edge pieces to the 56 border slots (orientation forced), and the
remaining 195 free interior pieces (196 minus the pinned clue) each take one
of 4 rotations.
No piece is rotation-symmetric. Every one of the 256 pieces has 4
distinct orientations, so rotation never shrinks a piece's candidate set.
No two pieces are identical, even up to rotation. There are no
interchangeable duplicates to exploit.
Five pairs share a colour multiset without being the same piece: pieces
3 & 4, 6 & 15, 8 & 52, 110 & 111, 172 & 182 (1-based official numbering)
carry the same four colours in a different cyclic order.
The clues break all board symmetries. A 16×16 board has no centre cell,
so every rotation or reflection moves the mandatory clue square I8: no
non-trivial symmetry maps the clued puzzle to itself, and symmetry-breaking
offers no further search-space reduction.
The 256 pieces carry 1,024 edge stickers; 64 are grey (2 per corner piece,
1 per edge piece), leaving 960 coloured edge instances. Their census
(computed; see rare-colour geography):
Colour group
Colours
Edge instances each
Total
Frame-only ("rare")
5
24 (all on frame pieces, none interior)
120
Interior palette, low
5
48
240
Interior palette, high
12
50
600
All
22
960
Two consequences researchers keep rediscovering:
Every per-colour count is even, and the halves sum to exactly 480.
A matched internal edge consumes two instances of one colour, so a perfect
solution needs ∑cNc/2=480 matches, which is exactly the number
of internal edges. There is zero slack: in a full solution every single
edge instance of every colour finds its partner.
The five rare colours live only on the frame (24 instances each), which
makes the frame ring a nearly self-contained sub-puzzle; the geometry is
worked through in rare-colour geography.
computed: re-derived exactly from the official 256-piece set; the
relevant pages carry just research-… reproduction commands and the raw
results live in the repository.
groups.io: the record scores (468, 469, 470, the strict 464) exist only
in mailing-list messages and on the community board viewer; the exact
announcement messages are linked from Records & solvers,
and each board can be re-scored at e2.bucas.name.
Wikipedia: covers only the encyclopedic layer (the prize, the deadline,
and Verhaard's 467).