The possibility space of seven-letter honeycomb puzzles
Published for direct use; search approval pending. Its mechanically validated result is available, but the page remains noindex and outside sitemaps while human editorial and source-rights review is incomplete.
Result
57,581 seven-letter honeycomb-style configurations pass the v1 quality bar, drawn from 15,593 candidate alphabets over 98,009 eligible answer records in this build.
- Analysis population
- 98,009
- Kept honeycomb configurations
- 57,581
- Candidate seven-letter alphabets
- 15,593
- Eligible answer records
- 98,009
57,581 seven-letter honeycomb-style configurations pass the v1 quality bar, drawn from 15,593 candidate alphabets over 98,009 eligible answer records in this build.
What a viable configuration means here
Candidate alphabets are the exact lettersets of eligible records with seven distinct letters, so every kept configuration has at least one pangram by construction. Eligibility uses membership in the pinned ENABLE artifact and build-specific ranking tiers; it does not claim validity in any commercial word game, and the v1 answer-count and pangram thresholds are declared judgment calls.
Kept configurations by answer-count band
The adjacent band table lists every exact count and share.
Population and exclusions
| Population stage | Records (records) |
|---|---|
| Raw lexical ledger | 394595 |
| Excluded by product policy | 150 |
| Safe normalized-spelling records | 394445 |
| Records meeting this study's inclusion criteria | 98009 |
How large the possibility space is
| Measure | Count (items) |
|---|---|
| Eligible answer records | 98009 |
| Distinct exact lettersets | 37278 |
| Records using exactly seven distinct letters | 37858 |
| Candidate seven-letter alphabets | 15593 |
| Alphabets with at least one kept puzzle | 12772 |
| Kept (alphabet, center) configurations | 57581 |
Answer counts across kept configurations
| Answer-count band | Kept puzzles (puzzles) | Share of kept puzzles (percent) |
|---|---|---|
| 15-41 | 10589 | 18.39 |
| 42-68 | 16677 | 28.96 |
| 69-95 | 16899 | 29.35 |
| 96-120 | 13416 | 23.30 |
Required center letters
| Center letter | Kept puzzles (puzzles) | Share of kept puzzles (percent) |
|---|---|---|
| a | 2551 | 4.43 |
| b | 2249 | 3.91 |
| c | 3513 | 6.10 |
| d | 2163 | 3.76 |
| e | 2274 | 3.95 |
| f | 1743 | 3.03 |
| g | 2373 | 4.12 |
| h | 2910 | 5.05 |
| i | 4352 | 7.56 |
| j | 239 | 0.42 |
| k | 1821 | 3.16 |
| l | 3023 | 5.25 |
| m | 2348 | 4.08 |
| n | 3470 | 6.03 |
| o | 3745 | 6.50 |
| p | 2045 | 3.55 |
| q | 200 | 0.35 |
| r | 2608 | 4.53 |
| s | 1306 | 2.27 |
| t | 2537 | 4.41 |
| u | 3772 | 6.55 |
| v | 1124 | 1.95 |
| w | 1430 | 2.48 |
| x | 428 | 0.74 |
| y | 2789 | 4.84 |
| z | 568 | 0.99 |
Pangram counts
| Pangram count | Kept puzzles (puzzles) | Share of kept puzzles (percent) |
|---|---|---|
| 1 | 40404 | 70.17 |
| 2 | 11769 | 20.44 |
| 3 | 3277 | 5.69 |
| 4 | 1212 | 2.10 |
| 5-or-more | 919 | 1.60 |
Hardest and easiest kept configurations by answer count
| Group | Rank | Seven-letter alphabet | Required center | Answers (records) | Pangrams (records) | Point ceiling (points) | Tier 1-2 answers (records) | Tier 1-2 answer share (percent) |
|---|---|---|---|---|---|---|---|---|
| hardest | 1 | abcdhkn | c | 15 | 1 | 68 | 8 | 53.33 |
| hardest | 2 | abcdkrw | w | 15 | 2 | 69 | 7 | 46.67 |
| hardest | 3 | abceopu | u | 15 | 1 | 60 | 7 | 46.67 |
| hardest | 4 | abciouv | i | 15 | 1 | 74 | 4 | 26.67 |
| hardest | 5 | abdeorx | x | 15 | 2 | 101 | 3 | 20.00 |
| easiest | 1 | abcdehs | h | 120 | 1 | 640 | 43 | 35.83 |
| easiest | 2 | abcdnor | a | 120 | 1 | 537 | 62 | 51.67 |
| easiest | 3 | abcefks | s | 120 | 1 | 500 | 44 | 36.67 |
| easiest | 4 | abcehir | c | 120 | 1 | 644 | 36 | 30.00 |
| easiest | 5 | abcehnt | t | 120 | 1 | 512 | 51 | 42.50 |
Methodology
Research question: How many viable seven-unique-letter honeycomb-style puzzle configurations does this lexical release support, and how are answers and pangrams distributed across them?
Why it is useful: The counts show how letterset and center choice change answer and pangram totals in this build; the tier-share metric is only a declared difficulty proxy, not measured human difficulty.
Included
honeycomb-possibility-space.answer-eligibility: Include safe normalized spellings of at least four letters, at most seven distinct letters, ranking tier three or better, with membership in the pinned ENABLE artifact.honeycomb-possibility-space.alphabet-source: Candidate alphabets are the exact lettersets of included records with exactly seven distinct letters, so every candidate has at least one pangram.
Excluded
honeycomb-possibility-space.product-policy: Exclude spellings matched by the exact first-party content-safety policy before enumeration.honeycomb-possibility-space.quality-bar: Exclude (alphabet, center) configurations outside the declared v1 window of 15 to 120 answers or without a pangram.
Transformations
honeycomb-possibility-space.letterset-fold-v1: Group included records by exact letterset, fold submask aggregates into per-center answer, pangram, and point totals, and keep configurations passing the declared v1 quality bar.
Calculations
research.count-v1- Count eligible records, candidate alphabets, or kept configurations in each declared group. Formula:
count(records). research.share-v1- Calculate the exact share of kept configurations, or of a configuration's answers, in a declared group. Formula:
100 * group_count / group_denominator. research.score-ceiling-v1- Sum every answer's declared base points plus a fixed bonus per pangram for one configuration. Formula:
sum(answer_points) + pangram_bonus * pangrams.
Limitations
- Eligibility uses membership in one pinned game-history artifact and build-specific ranking tiers; it does not establish validity in any commercial word game.
- Answer counts describe this exact normalized build and change with any source or policy update.
- The tier 1-2 answer share is a build-specific ranking proxy, not a measured human difficulty.
- The aggregate download lists lettersets and counts only; it does not redistribute answer word lists.
Versions, sources, and review
enable artifact-sha256:d3fbe8485022088fcf527edcde2fbdc18b4bbc141ac58123c9adb462e086eaf7
source-membership; surface-spelling-as-listed.
Licence: Licence terms not stated by the source. Legal review: pending. Redistribution review: pending.
- The downloaded artifact is content-pinned by SHA-256, but it contains no licence notice and the configured source page does not state reuse terms.
- The artifact is reproducibly pinned but no affirmative reuse grant has been located; redistribution approval remains pending.
- Dialect or scope: North-American-oriented; exact edition metadata unavailable
ENABLE (Enhanced North American Benchmark Lexicon); exact reuse terms are pending legal review
frequencywords-en-2018 git:525f9b560de45753a5ea01069454e72e9aa541c6; corpus-release:2018
source-token-observation; source-token-count.
Licence: CC BY-SA 4.0 (content). Legal review: pending. Redistribution review: pending.
- The exact pinned README states MIT for code and CC BY-SA 4.0 for content. Human review is required for attribution and ShareAlike obligations on compiled and derived data.
- Content is declared CC BY-SA 4.0. Attribution and ShareAlike treatment of the compiled frequency evidence and derived tiers require human approval.
- Dialect or scope: unspecified
FrequencyWords content derived from OpenSubtitles, licensed CC BY-SA 4.0
offensive-term-policy 2026.07-review-pending.2
content_filter; search_results; result_counts.
Licence: Reuse terms not yet approved. Legal review: pending. Redistribution review: pending.
- This bounded policy list cannot determine whether every usage is offensive or benign.
The Word Index first-party content-safety exclusion policy
Citations
- The Word Index pinned lexical source manifest, The Word Index, version 2026.07-lexical.6 (dataset).
- ENABLE word list, wordgamedictionary.com mirror, version artifact-sha256:d3fbe8485022088fcf527edcde2fbdc18b4bbc141ac58123c9adb462e086eaf7 (dataset).
- FrequencyWords English 2018, FrequencyWords, version git:525f9b560de45753a5ea01069454e72e9aa541c6; corpus-release:2018 (dataset).
- The Word Index content-safety exclusion policy, The Word Index, version 2026.07-review-pending.2 (policy).
Data and reproducibility
Source-rights review is pending. The available file contains aggregate computed measures, not a redistributed spelling list. Availability does not grant broader reuse rights; consult the source and licence register before reuse.
Download the canonical aggregate CSV
View the canonical JSON study bundle.
Reproduce this version from a clean checkout:
make studies_reproduce STUDY=honeycomb-possibility-space