---
slug: mastermind-five-guesses
passed: 2026-10-14
by: the assay line (research/assay-line/cited-1014b/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex and a Claude agent
checked: 87
confirmed: 81
wrong: 6
unverifiable: 0
observed: 0
stale: 0
---

This was the directed repair pass for mastermind-five-guesses at 7116b1331e. I re-read the evidence for all eight triage items, repaired the supported findings within this layer, and retained the checkers' other CONFIRMED claims from their review of 67088387e0, explicitly attributing those earlier readings and observations. Changed claims below use the repaired wording. The two rejected findings are CONFIRMED with the inference that supports rejection. The six findings count two WRONG and four MINOR triage lines, including duplicate reports of the same errors. The reciprocal secretary note in another layer remains outside the permitted edit scope. Prior live-site observations are not presented as a new deployment check.

## Claims

- MINOR | [X1 knuth-free-ties] Knuth minimax ties are free choices. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf; public/strata/mastermind-five-guesses/index.html | Re-read scan p. 3: Knuth resolves minimax ties by preferring a candidate and then numeric order. The implementation already uses this rule. Fixed the loose attribution in the page and README; same repair as K3.
- WRONG | [X2 nearby-secretary] Both problems separate the strategy that minimizes a uniform average from the one that protects a hard limit. | src/content/strata/look-then-leap.md; public/strata/look-then-leap/index.html | Re-read the best-choice and expected-rank passages: the first maximizes a probability, not a guaranteed outcome limit. Fixed the authored relation and regenerated this layer's nearby block. The reciprocal generated copy in look-then-leap remains NOT FIXED because another layer is outside the user's permitted scope. Same error as K6.
- MINOR | [K1 browser-rebuilds] The browser rebuilds this tree from scratch. | public/strata/mastermind-five-guesses/index.html; research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Re-read buildKnuth and its callers: the browser supplies code index 7 (1122). Qualified the explanation, loading message, legend, scope list and markdown. The verifier now derives every guess, including the opening, so its 1122 assertion is independent of the expected value.
- CONFIRMED | [K2 optimality-papers] Global optimality, both worst-case 5 and expected total 5,625, comes from exhaustive searches reported in the cited papers. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | REJECTED with evidence. Re-read sections 2 and 3: the exhaustive search establishes minimum total 5625 and a five-guess strategy. Inference: a four-guess guarantee would total at most 4 * 1296 = 5184, below 5625. Thus the searched minimum supplies the worst-case lower bound as well; no separate historical search is claimed.
- MINOR | [K3 knuth-free-ties] Knuth minimax ties are free choices. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf; public/strata/mastermind-five-guesses/index.html | Same re-read and repair as X1. Knuth p. 3 supplies the implemented tie rule; minimax as an objective alone leaves ties open. Credit now names Knuth, with no guessed explanation for differing published means.
- CONFIRMED | [K4 exhaustive-not-bound] Those are exhaustive-search theorems, not consequences of a naive information bound. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf; https://arxiv.org/pdf/1305.1010 | REJECTED with evidence. Koyama-Lai sections 2 and 3 establish 5625; Ville Table 8 gives the candidate-only minimum 5660. Inference: 5625 > 5184 excludes a four-guess guarantee. A naive 14-response information bound gives only ceil(log(1296)/log(14)) = 3. The alternative stronger counting argument uses actual first-guess partitions and does not contradict the page.
- MINOR | [K5 table-transcription] the embedded tree is a transcription of its Table 1. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf; public/strata/mastermind-five-guesses/index.html | Re-read Table 1, part C, PDF p. 5: the separator after 2(3446);0) is a semicolon. Restored that character. Both separators are accepted by the parser, so the tree and numerical results are unchanged.
- WRONG | [K6 nearby-secretary] Both problems separate the strategy that minimizes a uniform average from the one that protects a hard limit. | src/content/strata/look-then-leap.md; public/strata/look-then-leap/index.html | Same re-read and correction as X2; original checker_level was MINOR, directing triage raised it to WRONG. The secretary objective is best-choice probability or expected rank, not hard outcome protection. The authored relation and this layer's rendering are fixed; the reciprocal other-layer rendering remains outside scope.
- CONFIRMED | [#1 two-optima] Standard four-peg, six-colour Mastermind has two different optima. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.1: "Our strategy requires at most six guesses in the worst case and 5625/1296 ≈ 4.340 in expected case. We also show how to modify the strategy to use at most five guesses in the worst case; this increases the expected number of guesses to 5626/1296 ≈ 4.341." Ville p.4: "Minimizing W and minimizing E are two different goals." Excerpt present verbatim.
- CONFIRMED | [#2 dek] Run Knuth's minimax against all 1,296 secrets, then audit Koyama and Lai's published strategy tree: five guesses protects the worst case, while a sixth row buys the better average. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.3 excerpt present verbatim (six guesses only after 1123 (1,1), 1415 (1,1); the five-guess modification costs 5626 vs 5625). My own Knuth build: max 5; my replay of Table 1: max 6.
- CONFIRMED | [#3 plain-optimal] Mastermind strategy for the standard four-peg, six-colour game, where 'optimal' turns out to mean two different things. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: As #1.
- CONFIRMED | [#4 plain-strategies] Knuth's minimax cracks every one of the 1,296 secrets in at most five guesses; Koyama and Lai's tree needs fewer guesses on average (4.340) but takes a sixth row on one secret. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: Knuth p.3: "Fortunately this procedure guarantees a win in five moves." KL p.1: "5625/1296 ≈ 4.340". "One secret": my replay of the paper's Table 1 gives exactly one depth-six secret, 4421. The record cites only KL, which says nothing about Knuth's bound beyond p.1 "Knuth [1] demonstrated a strategy that requires at most five guesses in the worst case".
- CONFIRMED | [#5 plain-controls] Pick a hidden code, switch objectives, and watch the surviving set of candidates collapse after each scored guess. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: secret-peg click handlers, data-mode buttons calling updateMode(), renderRows() prints "N possible" on each row.
- CONFIRMED | [#6 seo-five] Mastermind Strategy: Why Five Guesses Are Enough | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: Knuth p.2: "The purpose of this note is to prove that the codebreaker can always succeed in five moves or less." KL p.3: "Note that any Mastermind strategy requires at least five guesses in the worst case."
- CONFIRMED | [#7 social-five] Five guesses protects the worst case. Allowing a sixth row wins on average. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: og:description and twitter:description (index.html lines 20, 28); as #2.
- CONFIRMED | [#8 social-operate] Operate both strategies. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: data-mode buttons "protect the worst case" and "lower the average" switch updateMode(), which renders knuthPath() or klPath().
- CONFIRMED | [#9 publication-date] "datePublished":"2026-07-26" | git show 67088387e0:src/content/strata/mastermind-five-guesses.md | Retained from the Claude checker at 67088387e0: frontmatter "date: 2026-07-26"; first commit 115036144b4 (2026-07-26); manifest runnable entry "firstPublished": "2026-07-26".
- CONFIRMED | [#10 modified-date] "dateModified":"2026-10-14" | public/strata/mastermind-five-guesses/index.html | This repair dates the content revision today; the earlier field was 2026-07-26. The dated correction already identifies the revision.
- CONFIRMED | [#11 md-computes] This interactive code machine computes Donald Knuth's five-guess minimax strategy from the fixed 1122 opening over every standard Mastermind secret, then audits Koyama and Lai's published expected-value tree. | public/strata/mastermind-five-guesses/index.html | buildKnuth fixes its opening to index 7, which encodes 1122, then recursively chooses minimax guesses; auditTable replays the published tree. K1 now qualifies that scope.
- CONFIRMED | [#12 md-controls] Choose a hidden code, switch objectives, and watch the surviving set collapse after each scored question. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: As #5.
- CONFIRMED | [#13 different-quantities] The two strategies optimize different quantities. | https://arxiv.org/pdf/1305.1010 | Retained from the Claude checker at 67088387e0: Ville p.4: "Minimizing W and minimizing E are two different goals." KL excerpt also present.
- CONFIRMED | [#14 tie-guarantee] Knuth guarantees no more than five rows using his published tie rule. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf; research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Knuth p. 3 supplies the candidate-first, numeric-order tie rule and five-move guarantee. The current verifier derives the opening and reproduces the maximum of five.
- CONFIRMED | [#15 md-optimum] Koyama and Lai's globally optimal expected-case tree totals 5,625 guesses across all 1,296 secrets (mean 4.340), but one secret needs a sixth row; replacing its vulnerable subtree raises the total to 5,626 and restores the five-row guarantee. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.2: "we performed an exhaustive depth-first computer search"; p.3: "The expected number of guesses for this modified strategy is 5626/1296 ≈ 4.341." My replay with K substituted for the 39-candidate 3155 node: [1, 8, 86, 654, 547], total 5,626, max 5.
- CONFIRMED | [#16 complete-tree] A complete search tree, opened and checked | git show 67088387e0:research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Retained from the Claude checker at 67088387e0: Reader-side run covers all 1,296 secrets in both trees; my replays cover all 1,296.
- CONFIRMED | [#17 scored-machine] The machine will ask only questions whose answers are scored by the ordinary black-and-white peg rule. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: gradeText() (line 746) matches the rule in Knuth p.1 and KL p.1 ("b(x, y) + w(x, y) is the number of pegs that are correct colors in either correct or incorrect positions").
- CONFIRMED | [#18 initial-audit] Building 1,296 codes and auditing both strategies. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: Loading placeholder; initialize() does this and replaces it.
- CONFIRMED | [#19 knuth-opens] Knuth opens 1122. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: Knuth p.2: "There are 1296 possibilities to start with. Your first test pattern should be 1122." Figure 1 (p.4) begins "1296(1122:". The record's excerpt (the p.3 tie-rule paragraph) does not contain 1122, and Figure 1 is on pp.4-5, not p.2.
- CONFIRMED | [#20 candidate-counter] The candidate counter is recomputed after every answer. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: knuthPath() and klPath() filter the candidates by the live score after each guess.
- CONFIRMED | [#21 full-search] The Knuth tree is being rebuilt from the fixed 1122 opening. | public/strata/mastermind-five-guesses/index.html | The loading message now states the actual browser scope: buildKnuth starts with build(all, 1, 7).
- CONFIRMED | [#22 minimax-definition] Knuth chooses the guess whose worst response leaves the fewest candidates. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: Knuth p.3: "Figure 1 was found by choosing at every stage a test pattern that minimizes the maximum number of remaining possibilities, over all 15 responses by the codemaker."
- CONFIRMED | [#23 tie-rule] Knuth's published tie rule prefers a remaining candidate, then the first code in numeric order. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf; public/strata/mastermind-five-guesses/index.html | Read the scan at p. 3 and chooseMinimax: the stated and implemented rule is Knuth's.
- CONFIRMED | [#25 kl-opens] Koyama and Lai's exhaustive search opens 1123. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: Table 1 p.5: "1296 (1123: 2 (2311), 44A, 222B, 276C, 81D;"; p.2 "we performed an exhaustive depth-first computer search".
- CONFIRMED | [#26 not-searching-table] The browser does not search for this tree. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: Only parseTable() and auditTable() touch it.
- CONFIRMED | [#27 table-audit] It expands their published Table 1, replays every edge, and rejects the table if one count or one score is inconsistent. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: auditTable() throws "Table count ... disagrees with live count", "Table shorthand failed", "Perfect-response count failed". The parser accepts ',' and ';' interchangeably (line 790): see #58.
- CONFIRMED | [#28 hist-all] All 1,296 secrets | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: Knuth p.1: "hence there are 6^4 = 1296 possible codewords".
- CONFIRMED | [#29 hist-recompute] Recomputing both distributions. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: Loading placeholder; renderHistogram() after initialize().
- CONFIRMED | [#30 hist-knuth-legend] Knuth minimax, rebuilt live from the fixed 1122 opening | public/strata/mastermind-five-guesses/index.html | The legend now discloses the browser's supplied opening; subsequent decisions are computed live.
- CONFIRMED | [#31 hist-kl-legend] Koyama and Lai, published tree audited live | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: auditTable() on the embedded Table 1.
- CONFIRMED | [#32 tail-saving] The expected-case tree moves enough secrets left to save 176 guesses in total against Knuth's published tie rule. | https://arxiv.org/pdf/1305.1010; research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Ville Table 3 and the current verifier give 5801 and 5625; their difference is 176. The copy now credits the tie rule to Knuth.
- CONFIRMED | [#33 sixth-leaf] It also grows one new leaf on row six. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: Table 1 F: "39 (3155: 1, 4 (1536), 8 (1346), 9 (1264: 1, 2 (2421)," ; my replay finds exactly one depth-six secret, 4421.
- CONFIRMED | [#34 sixth-route-audit] The published tree's only depth-six route is audited from its response edges. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: My replay: 1123 (1,1), 1415 (1,1), 3155 (0,1), 1264 (0,3), 2421 (3,0), 4421. The browser audit checks only that the depth-six list is "4421"; the route sentence is a fixed string in initialize() ('depth-six-path'). The verifier does check the full route.
- CONFIRMED | [#35 subtree-cost] Replacing the one vulnerable 39-candidate subtree with Koyama and Lai's published five-row modification costs exactly one extra guess across the entire code space. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.3: "K = 39 (1256: 1, 5 (6135), 10 (4335*), ..." and "5626/1296 ≈ 4.341"; replay 5,626 - 5,625 = 1.
- CONFIRMED | [#36 logical-definition] A guess is logical when it is still a possible secret. | https://supermastermind.github.io/playonline/optimal_strategy.html | Retained from the Claude checker at 67088387e0: KL defines candidates (p.2 "the set C of candidates") but never says "logical"; the term is the Super Mastermind page's: "Koyama and Lai's mathematically optimal strategy which allows playing illogical codes at each stage of the game".
- CONFIRMED | [#37 allows-ruled-out] Koyama and Lai allow a guess that earlier answers have already ruled out. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.3: "the presence of * denotes that y1 y2 y3 y4 is not a candidate"; Table 1 has 1515*, 3114*, 1461* and others; my replay finds 37 situations whose guess is not a candidate.
- CONFIRMED | [#38 false-guesses-inform] It cannot be the answer, but its pattern of responses can split the candidates more cleanly. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: Knuth p.3: "A codeword which cannot possibly win in four is necessary here in order to win in five." Excerpt matches the scan.
- CONFIRMED | [#39 false-example] For secret 6312, the strategy asks 2345 and then 2461; both are already impossible, and both still carry information. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: My replay of Table 1 part A: 1123 (0,3), 2345 (1,1), 2461 (0,3), 6312; two non-candidate guesses.
- CONFIRMED | [#40 illogical-counts] The live audit finds 539 secrets whose routes use at least one such question, and 121 routes that use two. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: My replay: 539 with at least one, 121 with two, maximum 2. Super Mastermind: "between 0 and 2 illogical codes are played at the second and/or third attempts".
- CONFIRMED | [#41 logical-optimum] If every guess must remain a candidate, the optimum rises from the unrestricted 5625 / 1296 = 4.340 to the logical-only 5660 / 1296 = 4.367. | https://supermastermind.github.io/playonline/optimal_strategy.html | Retained from the Claude checker at 67088387e0: "with an average number of attempts to find secret codes of 5660 ⁄ 6 4 ≈ 4.367 and a maximal number of attempts of 6" and "Koyama and Lai's mathematically optimal strategy which allows playing illogical codes at each stage of the game ( 5625 ⁄ 6 4 ≈ 4.340". The tool's PARTIAL is the superscript rendered as "6 4"; the text is there.
- CONFIRMED | [#42 logical-published] The 35-row penalty is a published exhaustive-search result; | https://arxiv.org/pdf/1305.1010 | Retained from the Claude checker at 67088387e0: The Super Mastermind page gives 5660 but not its method. Ville (cited on the page) gives it from his branch-and-bound program: Table 8 "Optimal path lengths in the expected case for MM*(p,c)", row p=4, column c=6: "5,660" (PDF p.18). 5,660 - 5,625 = 35.
- CONFIRMED | [#43 no-logical-tree] this page demonstrates the ruled-out guesses but does not reconstruct that separate logical-only tree. | git show 67088387e0:research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Retained from the Claude checker at 67088387e0: No logical-only table is embedded; the verifier checks only "published logical-only arithmetic".
- CONFIRMED | [#44 score-rule] Scores count exact positions first, then colour matches among the unused pegs. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: gradeText() line 746.
- CONFIRMED | [#46 uniform-averages] Averages assume all 1,296 secrets are equally likely. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.1: "If each secret code is equally probable"; the page divides every total by 1296.
- CONFIRMED | [#48 own-tie-result] This page follows Knuth's published tie rule and prints its computed result. | public/strata/mastermind-five-guesses/index.html; https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | chooseMinimax uses the rule on Knuth p. 3, and initialize prints the resulting histogram, total and mean.
- CONFIRMED | [#49 no-sampling] No sampling, physical measurement, uncertainty interval, or toy model is used. | git show 67088387e0:research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Retained from the Claude checker at 67088387e0: Full enumeration; the only randomness is the "Choose another secret" button.
- CONFIRMED | [#50 independent-score] Waiting for the independent scoring pass. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: Loading placeholder replaced by the audit line in initialize().
- CONFIRMED | [#51 local-scope] Locally recomputed: the scoring function, the 1,296-code space, all 14 attainable responses, the deterministic Knuth tree from the fixed 1122 opening, every candidate count in the Koyama-Lai table, every response edge, both histograms, the sole depth-six secret, every ruled-out guess, and the one-row cost of substituting the published five-row subtree. | public/strata/mastermind-five-guesses/index.html | The browser computation starts from a fixed opening. K1 repairs the scope wording; the subsequent tree construction and table audit remain as checked by both reviewers.
- CONFIRMED | [#52 cited-worst] that no worst-case strategy can do better than five | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.3: "Note that any Mastermind strategy requires at least five guesses in the worst case." Ville p.4: "W (4, 6) = 5 in fact".
- CONFIRMED | [#53 cited-average] that no expected-case strategy totals fewer than 5,625 rows | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.3: "Below, we describe our optimal Mastermind strategy. Our strategy uses 5625/1296 ≈ 4.340 guesses in the expected case"; Ville p.4: "the optimal value of E for MM(4,6) is E(4, 6) = 5625/1296 = 4.340".
- CONFIRMED | [#54 cited-logical] that the best candidate-only tree totals 5,660. | https://supermastermind.github.io/playonline/optimal_strategy.html | Retained from the Claude checker at 67088387e0: Excerpt present; also Ville Table 8 (PDF p.18), MM*(4,6) "5,660".
- CONFIRMED | [#56 citation-knuth] D. E. Knuth, “The Computer as Master Mind”, Journal of Recreational Mathematics 9(1), 1976-77, pp. 1-6. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: Scan p.1: "J. RECREATIONAL MATHEMATICS, Vol. 9(1), 1976-77", "THE COMPUTER AS MASTER MIND", "DONALD E. KNUTH"; pages numbered 1 to 6. The page links https://janmr.com/refs/knuth-mastermind76/, which links this scan.
- CONFIRMED | [#57 citation-koyama] K. Koyama and T. W. Lai, “An Optimal Mastermind Strategy”, Journal of Recreational Mathematics 25(4), 1993, pp. 251-256; | https://arxiv.org/pdf/1305.1010 | Retained from the Claude checker at 67088387e0: Ville ref [12]: "Kenji Koyama and Tony W. Lai. An optimal Mastermind Strategy. Journal of Recreational Mathematics, 25(4):251–256, 1993." It is on PDF p.20, not p.19 as the record says. The linked KL PDF is a 6-page layout without journal pagination.
- CONFIRMED | [#59 citation-ville] G. Ville, “An Optimal Mastermind (4,7) Strategy and More Results in the Expected Case”, 2013. | https://arxiv.org/abs/1305.1010 | Retained from the Claude checker at 67088387e0: "[Submitted on 5 May 2013]"; citation_title and citation_author "Ville, Geoffroy" match.
- CONFIRMED | [#60 citation-project] Super Mastermind optimal-strategy table | https://supermastermind.github.io/playonline/optimal_strategy.html | Retained from the Claude checker at 67088387e0: "Code Breaker games (4 columns, 6 colors)" table: "1233 4.367 (5660)".
- CONFIRMED | [#61 crosschecked-table] The candidate-only total is cross-checked against the Super Mastermind optimal-strategy table. | https://supermastermind.github.io/playonline/optimal_strategy.html | Retained from the Claude checker at 67088387e0: Page's 5660 equals the table's; the verifier holds 5660 as a constant and checks the arithmetic.
- CONFIRMED | [#62 verifier-path] The standalone verifier is research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs. | git show 67088387e0:research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Retained from the Claude checker at 67088387e0: Exists; served at /checks/research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs (200, 17,214 bytes).
- CONFIRMED | [#63 one-table] It reads this embedded table rather than keeping a second hidden copy. | git show 67088387e0:research/mastermind-five-guesses/verify-mastermind-five-guesses.mjs | Retained from the Claude checker at 67088387e0: Lines 138-139 read index.html and parse script#kl-data; EXPECTED holds totals only, no table.
- CONFIRMED | [#64 reads-bytes] This layer's check reads the bytes this page serves and asserts against them. | https://artwaste.land/checks/ | Retained from the Claude checker at 67088387e0: Reader-side run on the downloaded live page: exit 0, 35 PASS lines.
- CONFIRMED | [#66 same-reader-bytes] It is reading what you are reading. | https://artwaste.land/strata/mastermind-five-guesses/ | Retained from the Claude checker at 67088387e0: Live page equals the pinned file except the injected pulse and analytics scripts; the recipe downloads that URL.
- CONFIRMED | [#67 published-two-files] It is published, and it runs from 2 files this site serves | https://artwaste.land/checks/ | Retained from the Claude checker at 67088387e0: Lists "runs 2 files" with two curl lines and the node command; run in an empty directory: exit 0.
- CONFIRMED | [#69 nearby-nim] Two solved games reveal how a compact decision rule can outperform intuition across every possible state. | git show 67088387e0:src/content/strata/the-strategy-that-counts-in-binary.md | Retained from the Claude checker at 67088387e0: Dek: "it has been completely solved since 1901, when Charles Bouton proved that the whole strategy is one number".
- CONFIRMED | [#71 nearby-monty] Both expose optimal as a conditional word whose meaning changes when the question changes. | git show 67088387e0:src/content/strata/monty-hall.md | Retained from the Claude checker at 67088387e0: Dek: "The famous answer isn't a fact about doors: it's a fact about what the host knew."
- CONFIRMED | [#72 live-success] Audit passed: 1,296 / 1,296 secrets | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: Set only after the regression checks in initialize() pass; my replays agree on every total.
- CONFIRMED | [#73 live-definition] Definition, recomputed 6^4 = 1,296 codes. 14 attainable black/white responses. Scores count exact positions first, then colour matches among the unused pegs. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL p.1: "Note that there are 14 possible hints."; Knuth p.2: "Note that it is impossible to have three black hits and one white hit." My scorer: 14 responses over 1,679,616 pairs.
- CONFIRMED | [#74 live-hist-summary] All 1,296 secrets Knuth 5,801 total rows; expected-case tree 5,625. Difference: 176. | https://arxiv.org/pdf/1305.1010 | Retained from the Claude checker at 67088387e0: Ville Table 3: 5,801 and 5,625; my recomputation agrees.
- CONFIRMED | [#75 live-diagnostics] Knuth: [1, 6, 62, 533, 694], total 5801, mean 4.476080, max 5. Koyama-Lai: [1, 8, 86, 656, 544, 1], total 5625, mean 4.340278, max 6. Five-row substitution: [1, 8, 86, 654, 547], total 5626, mean 4.341049. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: All three recomputed independently: Knuth by my own minimax; Koyama-Lai and K from the paper's Table 1 text, not the page's JSON.
- CONFIRMED | [#76 live-audit-line] scoring pairs: 1,679,616 / Koyama-Lai decision situations: 937 / inconsistent response edges: 0 / depth-six secrets: [4421] / ruled-out-guess situations: 37 / most ruled-out guesses on one route: 2 | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: 1296^2 = 1,679,616; my replay: 37, [4421], max 2. The 937 is every table entry the audit visits (360 with a guess, 304 with one candidate, 273 empty); KL also calls n ≤ 1 entries situations (p.3 "the situation is represented by n if n ≤ 1"), so the count follows the paper's notation.
- CONFIRMED | [#77 live-depth-six] The sixth-row secret 4421 1123 gives 1 exact and 1 colour; 1415 gives 1 and 1; 3155 gives 0 and 1; 1264 gives 0 and 3; then 2421, then 4421. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: Matches my replay route (see #34).
- CONFIRMED | [#78 live-constrained] Forbid row six 5,626 / 1,296 | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: KL "5626/1296 ≈ 4.341"; replay 5,626.
- CONFIRMED | [#79 live-controls-kl] Koyama and Lai open 1123. Every route comes from their published Table 1. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: Table 1 "1296 (1123:"; klPath() walks the parsed table.
- CONFIRMED | [#80 live-candidates-recomputed] Candidate counts and responses were recomputed live. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: knuthPath()/klPath() use live scores and filters.
- CONFIRMED | [#81 live-motion] Reduced-motion mode renders one complete static state. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: renderRows() reduce branch appends every row at once.
- CONFIRMED | [#82 live-survive] This 5-row Knuth case collapses 1,296 to 256 to 44 to 7 to 1. No secret reaches row six. | https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/knuth-mastermind.pdf | Retained from the Claude checker at 67088387e0: My own build for 3631: 1122, 2344, 3516, 1461, 3631 with [1296, 256, 44, 7, 1]; depth-six count 0. Knuth's own example (p.2-3) shows the same 1296, 256, 44, 7 collapse.
- CONFIRMED | [#83 live-gold] Gold rows are questions the previous answers have already ruled out as secrets. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: Rows with logical false get class false-question (border #d6a638, line 239) and "ruled out already".
- CONFIRMED | [#84 browser-citation-boundary] Cited rather than re-run in the browser: | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: None of the three cited results is computed in the page.
- CONFIRMED | [#85 default-found-message] Secret 3631 found in 5 rows. Candidate counts and responses were recomputed live. | git show 67088387e0:public/strata/mastermind-five-guesses/index.html | Retained from the Claude checker at 67088387e0: Path length 5 recomputed (#82).
- CONFIRMED | [#86 false-example-found-message] Secret 6312 found in 4 rows. Candidate counts and responses were recomputed live. | https://prodigious.blog/wp-content/uploads/2025/08/optimal-mastermind-strategy.pdf | Retained from the Claude checker at 67088387e0: Replay depth 4 for 6312 (#39).
- CONFIRMED | [#added added-knuth-mean] In "protect the worst case" mode the page shows Knuth's minimax with mean guesses 4.476080 (5,801 / 1,296) and worst case 5 rows. | https://arxiv.org/pdf/1305.1010 | Retained from the Claude checker at 67088387e0: Ville p.7: "Knuth [10] showed that a guess that would minimize the maximum number of codes in each of k subsets (Max. size algorithm ...) has an average of 5801/1296 = 4.476", and Table 3 "Max. size 1122 5,801 4.476 5". KL p.1 gives "4.478" for Knuth's strategy; the page never prints 4.478.

## Findings

- [fixed] X1: narrowed the free-choice statement to minimax alone, credited Knuth's published tie rule throughout the owned prose and verifier labels, and removed the README's unsupported explanation of the 4.478 comparison. This MINOR repair has no public dated line.
- [fixed] X2: replaced the authored secretary relation with the supported change-of-objective comparison and regenerated this layer's nearby block. Added one Corrected line in HTML and markdown. NOT FIXED: public/strata/look-then-leap/index.html retains the reciprocal copy because the user forbids editing another layer; no claim is made that every site-wide copy is repaired.
- [fixed] K1: disclosed the fixed 1122 opening in every owned description of the browser rebuild. Removed the verifier's forced opening, so its assertion now tests a minimax choice; refreshed the served verifier from its authored source. No public dated line for this MINOR.
- [fixed] K3: duplicate of X1, resolved by the same tie-rule attribution repair, recorded separately to retain one disposition per triage item. No additional correction line.
- [fixed] K5: restored the semicolon in embedded Table 1 part C, from 2(3446);0),9(1246: to 2(3446);0);9(1246:. The parser treats both separators alike. No public dated line for this MINOR.
- [fixed] K6: duplicate of X2, kept WRONG with checker_level MINOR noted above. The same authored relation, owned rendering and single dated correction are repaired. The reciprocal look-then-leap copy remains NOT FIXED under the explicit layer boundary.