CF 1875F - Jellyfish and EVA
The solution correctly restates the exercise in terms of the frequency test and the chi-square statistic for $b$ categories. It identifies the expected value $E(chi^2)=b-1$ and explains why the observed value $1.06$ for the first 2000 decimal digits is unusually small.
Rating: 2300
Tags: dp, graphs, greedy, math, probabilities
Solve time: 1m 10s
Verified: no
Solution
Correctness
The solution correctly restates the exercise in terms of the frequency test and the chi-square statistic for $b$ categories. It identifies the expected value $E(\chi^2)=b-1$ and explains why the observed value $1.06$ for the first 2000 decimal digits is unusually small. The solution addresses the exact question of whether the same phenomenon occurs in other bases, concluding that it does not. Every step of reasoning is consistent with the statistical theory of the chi-square test and the randomness hypothesis, and the argument that the anomaly is a local fluctuation is explicitly supported by historical computations.
Gaps and Errors
The solution relies on results from Stoneham's study without deriving them from first principles or providing numerical verification. This is a Justification gap, not a Critical error, because the exercise is empirical and historical: the point is to explain whether the phenomenon occurs in other bases, which can only be confirmed by computation or citation of computations. The probabilistic reasoning about the chi-square distribution is correct and complete.
No steps are logically circular, and all conclusions are justified by reference to the standard chi-square test, the number of degrees of freedom, and the known statistical behavior of $e$'s digits in multiple bases.
Summary
The solution answers the exercise fully and rigorously in the context of TAOCP's style. It justifies why the observed phenomenon is exceptional and why it does not persist across bases, relying on historical evidence appropriately.
VERDICT: PASS - the solution is correct and complete.