Model casually estimates C(734,15) at 7×10^30 in its head — true value 6.4×10^30

Singularitarian · x · 2026-11-12

Researcher Dominik Peters shares that the model Fable 5.2 casually estimated a large binomial coefficient C(734,15) ≈ 7×10^30 as a throwaway in an answer. Asked how, it explained it was a mental estimate — true value ≈ 6.4×10^30 (verified with math.comb) — walking through the reasoning: the numerator is 727^15 ≈ 8×10^42, divided by 15! ≈ 1.3×10^12, landing at 6–7×10^30. A 10% error from an offhand estimate is striking mental arithmetic.

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