# The variants and the claims that live there

> Every "Eternity II" that is not the real puzzle: the TopCoder Marathon variant and the unresolved Takahashi 468, McGavin's unframed 480/480, the mixed-set boards, the no-starter challenge, and the claim quarantine, from the 2007 phantom-sets warning to the community's zero-knowledge verification ethic. Ends with a checklist for stating a score properly.

- Canonical page (with interactive figures/demos): https://eternity2.dev/research/build/variants/
- Updated: 2026-07-02
- Source: The phantom-sets warning (Sergio Demian Lerner), eternity2@groups.io, 2007-07 — https://groups.io/g/eternity2/message/1210
- Source: The unsaved E2Lab "471" popup, eternity2@groups.io, 2009-12 — https://groups.io/g/eternity2/message/7284
- Source: A hand-solve worth "at least 472", never evidenced, eternity2@groups.io, 2010-01 — https://groups.io/g/eternity2/message/7383
- Source: Brendan Owen asks the 476/480 claimant to publish the grid, eternity2@groups.io, 2011-02 — https://groups.io/g/eternity2/message/8676
- Source: The $1000 no-starter challenge, quantified by Peter McGavin, eternity2@groups.io, 2011-06 — https://groups.io/g/eternity2/message/8924
- Source: The Vautrin "resolved" claim falls to duplicate-piece checks, eternity2@groups.io, 2014-10 — https://groups.io/g/eternity2/message/9300
- Source: The Takahashi 468 claim surfaces (Dima), eternity2@groups.io, 2017-09 — https://groups.io/g/eternity2/message/9694
- Source: The TopCoder rules check: randomly generated pieces (Peter McGavin), eternity2@groups.io, 2017-10 — https://groups.io/g/eternity2/message/9697
- Source: Unframed E2 solved: thousands of 480/480 boards (Peter McGavin), eternity2@groups.io, 2017-11 — https://groups.io/g/eternity2/message/9750
- Source: Why the unframed 480 is disqualified: grey edges not on the rim, eternity2@groups.io, 2017-11 — https://groups.io/g/eternity2/message/9766
- Source: The mixed-set "480": one E2 + Clue-1 + Clue-2 set (Peter McGavin), eternity2@groups.io, 2023-10 — https://groups.io/g/eternity2/message/11169

---
Over twenty years, the archive has accumulated a small zoo of puzzles that
are *almost* Eternity II: same pieces with a rule dropped, same rules with
different pieces, same board with donor pieces mixed in. Each variant is a
legitimate object of study (some produced genuinely beautiful results),
but each also became, sooner or later, the home address of a headline
score that is not a record on the real puzzle. This page is the field
guide: what each variant is, what was actually achieved on it, and how the
community learned to keep variant scores out of the
[records table](/research/records).

## Why variants matter: scores only compare within a game

There is one lesson, and everything else on this page is a case study of
it: **a score is only comparable to another score if both were achieved on
the same piece set under the same rules regime.** The real puzzle is the
board Tomy sold: 256 specific pieces, a 16×16 frame with the grey edges
on the rim, and the starter piece pinned at I8 (the four other clue
placements were optional aids under the contest rules,
[msg 11046](https://groups.io/g/eternity2/message/11046)). The record line
467 → 468 → 469 → 470 all lives in that one regime, verified board by
board ([msg 10554](https://groups.io/g/eternity2/message/10554)); the
strict five-clue line (best known: 464) is tracked separately because it
is a *harder* regime, not a different puzzle
([Records & solvers](/research/records)).

Change the piece set and "480" can become easy. Drop the frame rule and
480/480 has actually been *achieved*. Drop the starter constraint and the
expected number of solutions multiplies by 784. None of those numbers says
anything about the official 480, which remains unfound. Hence the
catalogue below, and the quarantine that follows it.

## The catalogue

### The TopCoder Marathon variant and the Takahashi 468 claim

In 2009, TopCoder ran a Marathon Match on an Eternity-II-*style* problem.
When Peter McGavin checked the contest's problem statement years later, he
found that it used **randomly generated pieces**, apparently with
different colour counts than E2 and possibly no distinction between border
and interior edge types
([msg 9697](https://groups.io/g/eternity2/message/9697)). Each test was
its own puzzle. That makes any score from the contest a statement about
random instances of the puzzle *class*, not about Monckton's fixed 256
pieces: a different game, however similar the rules sheet looks.

The claim attached to it surfaced in September 2017, in the afterglow of
McGavin's [10×10 benchmark](/research/build/benchmarks) solve: Dima
reported that "467 has been broken in 2009". Naohiro Takahashi (chokudai),
a top competitive programmer, had tweeted a 468. Dima stated plainly that
he had never seen the solution and it was unverified
([msg 9694](https://groups.io/g/eternity2/message/9694),
[9696](https://groups.io/g/eternity2/message/9696)). The scrutiny followed
the standard protocol. McGavin, surprised that a "simple" beam-search-style
method would beat everything in
[Verhaard's arsenal](/research/lab/experiments/louis-verhaard/eii)
([msg 9695](https://groups.io/g/eternity2/message/9695)), did the rules
check above and asked for confirmation that the 468 used the original
pieces ([msg 9697](https://groups.io/g/eternity2/message/9697)). David
Barr argued the other side: the tweet says "Eternity 2", and Takahashi's
own profile distinguishes the TopCoder contest from the real puzzle
([msg 9698](https://groups.io/g/eternity2/message/9698)). Dima undertook
to contact him and ask for the solution: "This is the only way to know
for sure" ([msg 9700](https://groups.io/g/eternity2/message/9700)).

No resolution ever appeared in the archive, so the claim's status remains
unresolved. Told in full: *if* the 468 was on the TopCoder variant, it is
rule-incomparable with Verhaard's 467; *if* it was on the real pieces, no
board was ever produced. Either way it stays out of the records table as
a claim, not a record.

### Unframed E2: McGavin's 480/480 that isn't a solution

The most beautiful non-result in the archive. In late 2017 Peter McGavin
set himself a variant: place **all 256 real pieces** on the real 16×16
board, but treat the grey edges as ordinary colours (so the border pieces
migrate into an interior band) and maximize internal joins. On 2 November
he posted 479/480
([msg 9736](https://groups.io/g/eternity2/message/9736)); ten days later
one of his backtrackers, working from around its 4,400th 14×15
sub-solution, found not one but **thousands of full 480/480
configurations**
([msg 9750](https://groups.io/g/eternity2/message/9750), picture at
[9755](https://groups.io/g/eternity2/message/9755)). Henk van der Griendt
laid the pieces out physically and confirmed they fit
([msg 9754](https://groups.io/g/eternity2/message/9754)).

The inevitable question came: so you have solved Eternity 2? McGavin
was precise. The board scores 480/480 internal joins with original pieces
on the original board, but "the competition rules say the grey edges must
be around the border, which clearly they are not. From that point of view,
the entry is disqualified"
([msg 9757](https://groups.io/g/eternity2/message/9757),
[9766](https://groups.io/g/eternity2/message/9766)). His own summary is
the model of how to report a variant result: "I set my own E2-like
challenge with my own rules and then solved it"
([msg 9767](https://groups.io/g/eternity2/message/9767)). He estimated the
variant's difficulty as on par with building an unframed 14×14 from the
196 middle pieces
([msg 9719](https://groups.io/g/eternity2/message/9719)). Hard, but
demonstrably not E2-hard: the frame constraint the variant drops is
precisely where the real puzzle's difficulty concentrates.

### Mixed piece sets: the donor-piece "480"s

The third family keeps the frame rule and changes the pieces. In 2014
McGavin showed complete 16×16 boards built from *two* E2 sets, exploiting
duplicate pieces ([msg 9305](https://groups.io/g/eternity2/message/9305)),
and in October 2023 he built a full 480/480 board from the pieces of one
E2 set, one Clue-1 set and one Clue-2 set
([msg 11169](https://groups.io/g/eternity2/message/11169)), in Vlastislav
W.'s max-distinct-tiles challenge, a deliberate game whose metric is how
many *distinct* official tiles such a board can carry (record: 238,
[msg 11167](https://groups.io/g/eternity2/message/11167),
[11170](https://groups.io/g/eternity2/message/11170)). These
constructions hide nothing: clearly labelled by their makers, they are
the reason the records table carries a "variant" badge on its 2023 row.
The full story of the donor sets (what the clue puzzles were, and how
their pieces ended up in these boards) is on
[the clue puzzles page](/research/build/clue-puzzles).

### The no-starter variant and the $1000 challenge

In June 2011, list member ebeternity put up $1000 for a full E2 solution
**without** the piece-139 starter constraint, valid to the end of
September ([msg 8922](https://groups.io/g/eternity2/message/8922)). It was
the first post-contest cash on the table. McGavin immediately quantified
what the relaxation buys: an estimated **1.1527 × 10⁷ solutions without
the starter constraint versus 14,702 with it**, 784 times more needles,
yet the expected backtracker cost per solution barely moves (9.2766 × 10⁴²
nodes versus 9.2751 × 10⁴², best-known search order)
([msg 8924](https://groups.io/g/eternity2/message/8924)). Fewer
constraints, proportionally bigger haystack: the variant is 784× "easier"
in solution count and essentially unchanged in work.

Nobody claimed the money. The only "solve" that reached the thread was a
second-hand 480 claim promptly labelled bogus, occasioning Johannes
Lindé's summary of a decade of such claims: claimants become "quite
indignant (or silent) upon requests for proof"
([msg 8951](https://groups.io/g/eternity2/message/8951),
[8952](https://groups.io/g/eternity2/message/8952)).

### A different objective: most pieces placed, zero conflicts

Not every variant changes the pieces or the frame. Some change the *scoring
rule*, and the cleanest example is the max-conflict-free-placement objective:
instead of counting matched edges on a full board, count the most pieces you
can place so that **every** placed piece matches all its neighbours, leaving
holes rather than mismatches. The score is "pieces placed", not "edges matched",
and the two are not comparable: a board with a handful of holes says nothing
about how a full board built from the same search would score.

The frontier here is old and small, and it still belongs to Louis Verhaard. His
"Only seven holes" board from around 2008 places **249 of 256** pieces
conflict-free, with the seven holes clustered in the top band (rows 1 to 4). In
June 2026 Laurent Zamofing reached **248**, one short of it, by recombining the
community's published 467-edge boards as crossover donors
([msg 11890](https://groups.io/g/eternity2/message/11890),
[11901](https://groups.io/g/eternity2/message/11901)). What is striking is that
both boards hit a *proven local dead-end* at their score: Verhaard's seven holes
cannot be filled by the seven remaining pieces, and freeing a radius-6
neighbourhood around them still never reaches 250. That the residual holes always land in the same top band, under an
objective that has nothing to do with edge count, is its own small finding, and
it is [the mismatch geometry again](/research/why/mismatch-geometry): the damage
collects against whichever edge the search finishes on, whatever it is
optimising.

## The claim quarantine

Variants are one way a false "record" is born; the other is a claim with
no board attached. The community's response to both matured into a
protocol, and its history is worth telling because the quarantined claims
still circulate.

**The earliest form: the phantom-sets warning (2007).** Within days of the
launch, Sergio Demian Lerner warned the list about "phantom sets":
accepting a stranger's "random" E2-like benchmark could mean unknowingly
solving an isomorphic re-encoding of the real puzzle, and handing the
stranger a $2M solution
([msg 1210](https://groups.io/g/eternity2/message/1210)). The community
adopted the practice of publishing benchmarks with provenance and known
solutions ([msg 1213](https://groups.io/g/eternity2/message/1213)). The
insight generalizes: *a piece set you cannot verify is a claim you cannot
score*. Set-scrutiny was part of the culture before any famous fake
arrived.

**The 471 that was never saved (2009).** One morning Dominique Schaltz
reported that E2Lab had popped up a message box overnight saying 471, but
the score did not appear on his grid and the configuration was apparently
never saved ([msg 7284](https://groups.io/g/eternity2/message/7284)).
Within weeks it echoed through the list as "somebody touched 471"
([msg 7317](https://groups.io/g/eternity2/message/7317),
[7353](https://groups.io/g/eternity2/message/7353)). No board ever
existed. The episode is the cleanest illustration of why the rule is
*board or it didn't happen*: a faithfully reported software popup, once
detached from its caveats, circulated as a record.

**The ≥472 hand-solve (2010).** Faruk Barber reported completing the whole
board by hand with none of the clue pieces on their positions; Henk van
der Griendt computed the claim would be worth at least 472 after swapping
the starter into compliance
([msg 7383](https://groups.io/g/eternity2/message/7383),
[7385](https://groups.io/g/eternity2/message/7385)). Al Hopfer called it
"just silly": a genuine 472 would dwarf the known 467
([msg 7427](https://groups.io/g/eternity2/message/7427)). No evidence was
ever posted; the claimant was simultaneously offering his clue puzzles for
sale ([msg 7395](https://groups.io/g/eternity2/message/7395)).

**The 476-then-480 bloom (2011).** In January 2011 Alain Bidon claimed a
476/480 achieved without the starter piece in place; the original message
is missing from the archive export and survives only through replies
([msg 8247](https://groups.io/g/eternity2/message/8247)). The list
immediately re-scored it under the rules (at best 472 without the starter,
468 guaranteed after compliance). By February the claim had grown to
multiple hintless **480s**
([msg 8636](https://groups.io/g/eternity2/message/8636)) and hit what
one member called "the good old zero knowledge test". Brendan Owen's two
demands in that thread are still the model of the genre: "there is a bug
in your program. Actually place the real pieces"
([msg 8670](https://groups.io/g/eternity2/message/8670)), and "could you
please publish the grid of piece ids"
([msg 8676](https://groups.io/g/eternity2/message/8676)); Bruce made it
concrete: just turn each piece over and post the 16×16 list of the
numbers on the backs
([msg 8681](https://groups.io/g/eternity2/message/8681)). No grid ever
appeared. In the same season an anonymous "new algorithm" announcement was
met with the other standard challenge: prove it by solving
[Brendan's hint-free 10×10 benchmark](/research/build/benchmarks)
([msg 8262](https://groups.io/g/eternity2/message/8262),
[8264](https://groups.io/g/eternity2/message/8264)).

**The Vautrin affair (2014): the protocol working end to end.** Nicolas
Vautrin first claimed his program could prove E2 has *no* solutions,
retracted (a bug), then days later posted "eternity2 resolved ;)" while
withholding the solution because of a prize
([msg 9280](https://groups.io/g/eternity2/message/9280),
[9286](https://groups.io/g/eternity2/message/9286),
[9291](https://groups.io/g/eternity2/message/9291)). This time a checkable
artifact existed, a claimed solution to one of Brendan's benchmark
puzzles, and verification killed it in days: Conny Öström's editor found
**115 duplicate pieces** in it
([msg 9300](https://groups.io/g/eternity2/message/9300)), McGavin
exhibited one piece used five times
([msg 9301](https://groups.io/g/eternity2/message/9301)), Arnaud Carré
identified the exact bookkeeping bug
([msg 9308](https://groups.io/g/eternity2/message/9308)), and Vautrin
conceded ([msg 9303](https://groups.io/g/eternity2/message/9303)). Nobody
had to trust anybody: the grid was posted, so the grid could be checked.

The pattern across all five stories is the community's real institutional
knowledge. Claims die or survive on artifacts (a grid of piece ids, a
solved public benchmark, a checksum), never on reputation, enthusiasm or
plausibility. The 471, the ≥472 and the 476/480s must never enter the
records table; the Takahashi 468 waits outside it for a board; and the
Vautrin episode shows the same machinery clearing a genuine mistake in
four days.

## How to state a score properly

Distilled from the twenty years above, the checklist the archive
effectively enforces. A score means nothing without all four:

1. **Name the piece set.** Official 256-piece E2? A Brendan benchmark set
   (which one)? Random pieces? Mixed donor sets? If the set is private or
   unverifiable, it scores nothing; the
   [phantom-sets warning](https://groups.io/g/eternity2/message/1210) is
   about exactly this.
2. **Name the rules regime.** Framed with grey edges on the rim?
   Starter-only (the 467→470 record line), strict five-clue (the 464
   line), no-starter (the $1000 challenge), or unframed? Scores do not
   transfer between regimes: 784× more solutions is still not the same
   game.
3. **Post the board.** The 16×16 grid of piece ids with rotations:
   Brendan's demand, Bruce's "turn each piece over". A board can be
   re-scored by anyone; a number cannot. Every board on
   [the notable boards page](/research/community/boards) can be loaded and
   re-scored edge by edge in the [viewer](/viewer).
4. **Say who and when, with a link.** The records table only carries
   entries with a primary source; claims that live only in a popup, a
   tweet or a memory stay quarantined
   ([Records & solvers](/research/records)).

Set + regime + board, or it didn't happen.

## Related

- [Records & solvers](https://eternity2.dev/research/records) — Eternity II has never been solved, but fifteen years of community effort have pushed the best board to 470/480. Who holds what, how they did it, and why some headline "480" boards are not actually the real puzzle.
- [The four clue puzzles](https://eternity2.dev/research/build/clue-puzzles) — Tomy sold four small companion puzzles for Eternity II: solve one, submit the solution, and the official site revealed one piece's placement on the main board. What each puzzle was, the broken online checker, the eBay grey market, why puzzles 5 and 6 never came, and the clue puzzles' second life as complex-theory test cases and donor piece sets.
- [The notable boards](https://eternity2.dev/research/community/boards) — The famous Eternity II boards, treated as first-class citizens: Verhaard's prize-winning 467, the Blackwood record line to 470, the strict five-clue record to 464, and this project's own boards: who found each one, when, and what makes it structurally interesting. Every bundled board opens in the viewer.