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Fix corrupted answers in answerbench_v2.csv - #20

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rootkiller6788:fix-answerbench-v2-geometry004-numbertheory048
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Fix corrupted answers in answerbench_v2.csv#20
rootkiller6788 wants to merge 1 commit into
google-deepmind:mainfrom
rootkiller6788:fix-answerbench-v2-geometry004-numbertheory048

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Summary

Fixes the two data corruptions reported in #14 in imobench/answerbench_v2.csv.

Changes

  1. imo-bench-geometry-004 — the Short Answer was 45752, which is not a valid answer to "find the value of n". Restored to "4, 5" (n = 4 or n = 5), matching answerbench.csv (v1).
  2. imo-bench-number_theory-048 — the inequality in the Short Answer was flipped to ab \leq e^3. Restored to ab \geq e^3, matching answerbench.csv (v1) and the known answer to this Vietnam 1997 problem (ab ≥ e³).

Verification

  • Both v1 (answerbench.csv) and v2 (answerbench_v2.csv) agree on every other field for these two rows; only these two answer fields differ, and v1 carries the correct values.
  • The geometry answer "4, 5" is the standard result (n = 4 or n = 5 cities).
  • The number-theory answer ab ≥ e³ matches the published solution (e.g. AoPS thread for this problem).

Diff is two lines changed, one per row.

- geometry-004: restore answer "4, 5" (n = 4 or n = 5) instead of the
  corrupted value 45752.
- number_theory-048: restore inequality direction ab \geq e^3 (the
  answer was flipped to ab \leq e^3 in v2).

Both match answerbench.csv and the known Vietnam 1997 answer.
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