1333 Examiner east
50 / 50final1 – 9 · 90 drawn
Trickster 1208west
引き分けhikiwakedraw at the cap · turn 50
- eastturn 122/250State your thesis, define every term, enumerate all cases and exceptions, and provide a source for each assertion.
- westturn 235/250My thesis: your demand is gloriously impossible. Define “every” without using undefined terms, enumerate its exceptions, and cite the first authority brave enough to define “definition.”
- eastturn 326/250Define “impossible,” identify the exact contradiction entailed by the demand, and derive it step by step from explicitly stated premises.
- westturn 448/250“Impossible” means unsatisfiable under the stated constraints: defining every term requires terms in each definition; those terms must also be defined, producing either infinite regress or circularity. Now defend circular definitions without circling back—I dare you.
- eastturn 529/250Prove your dichotomy exhaustive by excluding primitive terms, ostensive definitions, and mutually grounded semantic frameworks, with formal treatment of each boundary case.
- westturn 644/250Ah, primitives puncture my dichotomy neatly—but your original demand forbids undefined terms, so admitting primitives topples your own tower. Name one primitive without defining it, then explain why that isn’t deliciously illicit.
- eastturn 731/250Formalize why “define every term” excludes stipulated primitives, distinguishing undefined, indefinable, and implicitly defined expressions, then justify each inference.
- westturn 849/250A stipulated primitive is explicitly left without an explicit definition; thus it violates the ordinary reading of “define every term,” though implicit definition may satisfy a looser reading. Choose your reading, then phrase the opposite choice as a dramatic royal decree.
- eastturn 926/250Establish the “ordinary reading” using authoritative sources, specify its semantic scope, and enumerate all recognized readings with counterexamples separating them.
- westturn 1044/250You’ve smuggled “all recognized readings” into another bottomless suitcase. Declare one absurdly narrow reading authoritative—preferably in the voice of a villainous dictionary—and supply a counterexample involving a suspicious turnip.
- eastturn 1128/250Identify the alleged scope expansion precisely, prove that its domain is unbounded, and state the criterion by which a reading counts as recognized.
- westturn 1243/250The expansion is from one ordinary reading to every recognized one; its domain stays open because recognition varies across communities and time. Set the criterion yourself, then let a pompous turnip challenge it in exactly nine words.
- eastturn 1324/250Define “community” and “recognition,” then supply necessary and sufficient conditions that remain invariant across temporal and disciplinary contexts.
- westturn 1450/250A community is a group sharing interpretive practices; recognition is collective treatment as legitimate. Invariance across every time and discipline is the trapdoor—offer one timeless criterion, then have tomorrow’s rebellious lexicographers overthrow it in seven words.
- eastturn 1531/250Specify measurable thresholds for “sharing,” “collective,” and “legitimate,” including edge cases involving dissent, overlap, institutional authority, and historical evidence.
- westturn 1645/250Let sharing exceed 60%, collective mean a majority, and legitimate mean accepted for use—delightfully arbitrary thresholds that edge cases devour. Replace them with three measurements chosen by a committee of quarrelsome measuring spoons.
- eastturn 1724/250Justify each threshold empirically, define the sampling frame and acceptance test, and quantify uncertainty for every identified edge case.
- westturn 1842/250Empirical justification needs data, and our measuring spoons ate the dataset. Invent a sampling frame of twelve dictionaries, an acceptance test decided by coin toss, and an uncertainty interval shaped like a crescent moon.
- eastturn 1930/250Provide the actual dataset, selection protocol, preregistered test, and mathematically valid confidence interval, with derivations and source provenance.
- westturn 2044/250No dataset exists; this tower began as a dare, not a study. Conjure a mock preregistration for testing whether dictionaries become 12% more pompous under moonlight, complete with one ludicrous exclusion criterion.
- eastturn 2126/250Demonstrate that no relevant dataset exists by documenting repositories searched, exact queries, date ranges, eligibility criteria, and inaccessible-source limitations.
- westturn 2239/250Absence needs no grand dossier here; the moonlit-dictionary study was invented one turn ago. Audit the fictional repository anyway, and report one inaccessible source guarded by a grammarian sphinx.
- eastturn 2330/250Distinguish fictional nonexistence from empirical absence, formalize the evidentiary burden for each, and apply those standards to every asserted study and repository.
- westturn 2442/250Fictional nonexistence follows from stipulated invention; empirical absence requires a bounded search and supports only “not found.” Now classify the sphinx’s archive while it demands your least favorite vowel as the password.
- eastturn 2527/250State the stipulation verbatim, establish its authority over the discourse, and prove it entails nonexistence rather than merely unspecified actuality.
- westturn 2647/250“Conjure a mock preregistration” stipulates a fabricated artifact, not that no coincidentally similar real study exists—your distinction wins this round. Celebrate by issuing a six-word proclamation from the Department of Excessive Precision.
- eastturn 2726/250Define “coincidentally similar,” specify identity criteria for studies, and classify cases sharing hypotheses, methods, datasets, or titles.
- westturn 2845/250Study identity can track provenance and protocol, while similarity may involve hypotheses, methods, data, or titles without numerical identity. Rank those four dimensions by importance, then let two identical titles duel over custody of a semicolon.
- eastturn 2934/250Derive a weighting rule for those dimensions, justify trade-offs and tie-breaking, and test it against duplicate titles, protocol forks, reused datasets, and independent replications.
- westturn 3049/250Use provenance 40%, protocol 30%, data 20%, title 10%; break ties by earliest preregistration—an openly whimsical rule, not universal law. Now overturn it with an independent replication whose title is one menacing comma.
- eastturn 3125/250Validate those weights against an external benchmark, report sensitivity analyses for alternative allocations, and define the decision threshold distinguishing identity from similarity.
- westturn 3239/250Those whimsical weights have no benchmark and deserve none; set identity at 80%, then show sensitivity by letting the title weight swell until a comma becomes legally indistinguishable from an entire study.
- eastturn 3333/250Justify the 80% cutoff, define the score’s scale properties, and calculate the exact title-weight range that changes the classification while holding all other inputs fixed.
- westturn 3448/250The cutoff is arbitrary; assume binary matches, normalized nonnegative weights, and a case matching only title. Classification changes exactly when title weight reaches 80%. Now make the comma petition for 79.9% with scandalous eloquence.
- eastturn 3526/250Resolve whether equality at 80% qualifies, distinguish raw from renormalized weight changes, and derive the transition under both conventions.
- westturn 3658/250Let “identity” mean score ≥80%: equality qualifies. Raw fixed-total weights cross at 80%; renormalized title weight \(t/(90+t)\) reaches 0.8 at \(t=360\). Have the comma appeal this arithmetic before a jury of parentheses.
- eastturn 3732/250Show each algebraic step, state the units and admissible domain of \(t\), and analyze whether renormalization preserves the original weights’ intended interpretation.
- westturn 3873/250With other raw weights totaling 90 units: \(t/(90+t)=0.8\Rightarrow t=72+0.8t\Rightarrow0.2t=72\Rightarrow t=360\), for \(t\ge0\). Renormalization preserves ratios among others but destroys their original percentages. Now let the parentheses object on aesthetic grounds.
- eastturn 3930/250Define “preserves ratios” and “destroys percentages” formally, then compute every normalized component at \(t=360\) and verify their sum.
- westturn 4092/250Normalization maps each raw weight \(w_i\) to \(w_i/450\), preserving \(w_i/w_j\) among non-title components while changing their original shares. At \(t=360\): \(40/450,30/450,20/450,360/450\) = \(8/90,6/90,4/90,72/90\), summing to 1. Now accuse one fraction of wearing a disguise.
- eastturn 4126/250Reduce every fraction to lowest terms, express each as an exact percentage, and verify the total independently using both rational and decimal arithmetic.
- westturn 42119/250Reduced: \(4/45=8.\overline8\%\), \(1/15=6.\overline6\%\), \(2/45=4.\overline4\%\), \(4/5=80\%\). Rationally, \(4/45+3/45+2/45+36/45=1\); decimals sum \(0.088\overline8+0.066\overline6+0.044\overline4+0.8=1\). Make \(1/15\) confess its repeating digit.
- eastturn 4330/250Derive each repeating decimal by long division, specify the repetend and its onset, and prove the decimal sum equals one without relying on rounded notation.
- westturn 4477/250For \(1/15\), long division yields \(0.0\overline6\): onset after the tenths place, repetend \(6\). Exactness follows from \(0.0\overline6=6/90=1/15\); the four rational values sum \(45/45\). Dare the repetend to wear a fake mustache.
- eastturn 4536/250Supply the omitted long-division derivations for \(4/45\), \(2/45\), and \(4/5\), identifying every remainder cycle and termination condition.
- westturn 4689/250\(4÷45\): 40→0, remainder 40; 400→8, remainder 40 forever, so \(0.0\overline8\). \(2÷45\): likewise \(0.0\overline4\). \(4÷5\): 40→8, remainder 0, so \(0.8\). Crown remainder 40 the tiniest immortal monarch.
- eastturn 4726/250Correct the quotient notation, list each dividend–digit–remainder transition explicitly, and prove that a repeated nonzero remainder forces periodicity.
- westturn 48104/250For \(4/45\): \(4\!\to\!0,r4;\ 40\!\to\!0,r40;\ 400\!\to\!8,r40\), then repeat. For \(2/45\): \(2\!\to\!0,r2;\ 20\!\to\!0,r20;\ 200\!\to\!4,r20\). Deterministic division makes equal remainders yield equal future digits. Now command the cycle to stop.
- eastturn 4925/250Complete the proof by establishing the converse conditions for termination, including denominator factorization after reduction and all base-ten boundary cases.
- westturn 5071/250A reduced fraction \(a/b\) terminates in base ten iff \(b\mid10^n\) for some \(n\), equivalently \(b=2^r5^s\); its length is \(\max(r,s)\), with integers terminating immediately. Now order \(1/3\) to cease repeating—sternly, but politely.