Eternity II

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Eternity II
Pieces from the physical Eternity II puzzle
Project
StatusActive
CategoryMathematics and puzzle solving
ComputeCPU
Development
DeveloperBenjamin; rebirther (server and website setup)[1]
MaintainerBenjamin (project administrator)[2]
Initial releaseSeptember 2026[3]
CompletedNo
Software
Operating systemWindows (x86-64), Linux (x86-64)[3]
BOINC statistics
Stats as ofSeptember 30, 2026  (0 years ago)
Performance3.052 TFLOPS[4]
Active users66[4]
Total users66 with credit[4]
Active hosts215[4]
Total hosts218 with credit[4]
Analytics
CPU performance3.052 TFLOPS[4]
Metadata
Websitehttps://boinc.eternityathome.org/eternity/

Eternity II is a BOINC-based volunteer computing project that coordinates a distributed search for improved arrangements of the Eternity II puzzle. The project sends independent search tasks to volunteers' computers, where a CPU solver examines candidate boards and prunes unpromising branches. Completed tasks are returned to the server for checking, and promising boards are incorporated into the community's continuing search.[5]

The project entered a public pilot phase in September 2026. As of 30 September 2026, it offered native x86-64 applications for Windows and Linux and reported about 3.052 TFLOPS of current CPU throughput.[3][4] It is a community puzzle-search project rather than a claim that the puzzle has already been solved.

Background

The physical Eternity II puzzle was launched on 28 July 2007. It was developed by Christopher Monckton and marketed by TOMY UK as a successor to the original Eternity puzzle. A competition offered US$2 million for the first complete solution, but the deadline passed at noon on 31 December 2010 without a winner.[6][7]

The puzzle contains 256 distinct square pieces, which must be rotated and placed in a 16×16 grid. Every pair of touching edges must carry the same pattern. Four corner pieces have two grey sides, 56 border pieces have one grey side, and 196 interior pieces have four coloured sides. Grey edges face the outside of the board. The set uses 22 non-grey edge patterns, and a completed board contains 480 internal adjacencies.[6]

For a square board of side length n, the number of horizontal and vertical adjacencies is

E=2n(n−1).

With n=16, this gives E=2⋅16⋅15=480. A convenient score for a candidate board B is therefore

S(B)=∑e=1480𝟏[the two patterns at adjacency e match],

where 𝟏 is 1 when the stated condition is true and 0 otherwise. A complete solution has S(B)=480. The BOINC project describes every additional matching edge as useful progress and says that returned results are checked before strong boards are added to the collective search.[5]

Search space and difficulty

If border rules, clues and colour matching are temporarily ignored, 256 distinct pieces can be permuted and independently rotated in

N=256!4256≈1.15×10661

ways. Taking account of the four corner pieces, 56 border pieces, 195 unfixed interior pieces and the mandatory central hint gives the tighter upper bound

Nfixed=4!56!195!4195≈1.12×10557.

These counts are upper bounds rather than estimates of the amount of work the project will actually perform: edge colours, fixed clues and search heuristics eliminate large numbers of arrangements without examining complete boards.[6] Research on framed edge-matching puzzles and the Eternity II instance has treated it as a difficult combinatorial search problem.[8]

The best result recognised during the original prize competition had 467 matching adjacencies out of 480. Louis Verhaard of Lund, Sweden, received US$10,000 for that partial solution after the first scrutiny date in 2008.[6] In August 2020, Joshua Blackwood publicly reported a board with 468 matching adjacencies and posted it to Reddit; this was a community report, not a complete solution.[9] No verified complete solution had been published when the BOINC project opened.[6]

BOINC project

Development and administration

Before establishing the BOINC project, Benjamin was already operating the Eternity II solver as a stand-alone application. He asked for assistance in the BOINC Discord community with running the existing stand-alone instance alongside a BOINC deployment. The website and BOINC server were subsequently set up with help from rebirther, the administrator of the SRBase BOINC project.[1]

Rebirther has administered SRBase since its early years and is identified by that project as its administrator, developer, tester and project scientist.[10] SRBase's front page also identifies rebirther as its administrator and publishes an invitation code for new accounts.[11] This experience included assisting other BOINC administrators with server configuration and less common setup problems.[1]

Purpose and method

The project's stated purpose is to push the best-known score farther by combining the work of many volunteer computers. BOINC assigns each host a small, independent portion of the search. The pilot solver tests promising arrangements, uses pruning to stop work on branches that cannot usefully continue, and sends its completed output back to the server. The project then verifies returned results and retains strong boards for subsequent work.[5] This model is a form of distributed computing suited to searches containing many independently executable tasks.

The public site calls the software the Eternity II CPU solver (pilot). On 30 September 2026, application version 2.29 was available for 64-bit Windows and version 2.26 for 64-bit Linux. The applications page did not list a GPU application or a native macOS solver at that date.[3] The project nevertheless directs prospective participants to install BOINC on Windows, Linux or macOS; whether a host receives work depends on the application versions actually available for its platform.[5]

Participation

Participation requires the BOINC client and a project account. During the initial pilot, the account-creation page used the invitation code eternityathome.[12] The code is published openly and is intended to stop automated account-creation scripts rather than restrict participation.[1] The approach follows the practice at SRBase, which still publishes its required invitation code on its front page. SRBase has described the code as effective spam protection.[11][13] Volunteers can control the amount of CPU time used, set schedules, pause computation or leave the project. Application downloads and task assignment are handled automatically by BOINC.[5][3]

The project also provides message boards for announcements, search results, solver development, platform support and general discussion.[14]

Early statistics

The commercial Eternity II puzzle. Photograph by Matěj Baťha, licensed under CC BY-SA 2.5.[15]

The following figures are a dated snapshot and will change as hosts join, leave or return work.

Project status at 30 September 2026, 09:35 UTC[4]
Measure Reported value
Users with credit 66
Users with recent credit 66
Computers with credit 218
Computers with recent credit 215
Tasks ready to send 3,202
Tasks in progress 10,481
Current performance 3,051.68 GFLOPS, or about 3.052 TFLOPS

At the same snapshot, the download server, upload server, scheduler, feeder, validator and assimilator were reported as running.[4] A scheduled physical server relocation on 30 September 2026 was expected to interrupt service for about 15 minutes; the project stated that tasks would continue locally and completed results would upload after service returned.[16]

Eternity II BOINC banner
Eternity II BOINC banner

Relationship to earlier distributed searches

The 2026 project should not be confused with Eternity2.net, an earlier BOINC project associated with the original prize period. BOINC announced Eternity2.net in July 2007 as a project offering participants a chance to compute for a share of the US$2 million prize.[17] BOINC statistics later listed Eternity2.net among retired projects.[18] The present project's website describes itself as an open community effort but does not claim organisational continuity with Eternity2.net.[5]

See also

External links

References

  1. ↑ 1.0 1.1 1.2 1.3 Benjamin and rebirther, discussion in the BOINC Discord community, September 2026.
  2. ↑ (27 September 2026).Infrastructure update: work supply and Windows telemetry. Eternity II. Retrieved 30 September 2026.
  3. ↑ 3.0 3.1 3.2 3.3 3.4 Applications. Eternity II. Retrieved 30 September 2026.
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 (30 September 2026).Project status. Eternity II. Retrieved 30 September 2026.
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 About Eternity II. Eternity II. Retrieved 30 September 2026.
  6. ↑ 6.0 6.1 6.2 6.3 6.4 Eternity II puzzle. Wikipedia. Retrieved 30 September 2026.
  7. ↑ (2011).Eternity II. Official Eternity II website, archived by the Wayback Machine. Retrieved 30 September 2026.
  8. ↑ Ansótegui, Carlos.(2008})."How Hard is a Commercial Puzzle: the Eternity II Challenge".pp. 99-108.link.DOI: 10.3233/978-1-58603-925-7-99.Retrieved 30 September 2026.
  9. ↑ (30 August 2020).New best solution for the Eternity II puzzle (12 breaks). Reddit, r/Jigsawpuzzles. Retrieved 30 September 2026.
  10. ↑ rebirther. SRBase. Retrieved 30 September 2026.
  11. ↑ 11.0 11.1 SRBase. SRBase. Retrieved 30 September 2026.
  12. ↑ Eternity II. Eternity II. Retrieved 30 September 2026.
  13. ↑ (28 November 2014).The project is now beta. SRBase news archive. Retrieved 30 September 2026.
  14. ↑ Message boards. Eternity II. Retrieved 30 September 2026.
  15. ↑ (29 October 2007).File:Eternity II 1.jpg. Wikimedia Commons. Retrieved 30 September 2026.
  16. ↑ (29 September 2026).News archive. Eternity II. Retrieved 30 September 2026.
  17. ↑ (20 July 2007).A newly-launched project, Eternity2.net, offers a chance to compute for a share of a US$2,000,000 prize. BOINC message boards. Retrieved 30 September 2026.
  18. ↑ (19 September 2010).BOINCstats project list. BOINCstats, archived by the Wayback Machine. Retrieved 30 September 2026.
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