Question
Alan Turing’s final publication concerns some numerical approximations for solving this problem, which he had earlier cited as a “number theoretic theorem” in his Ph.D. thesis. For 10 points each:
[10e] Name this unsolved problem that asserts that the real part of every non-trivial zero of the zeta function is one-half.
ANSWER: Riemann hypothesis [or RH]
[10m] The Riemann hypothesis is computationally equivalent to a Turing machine with 29 of these things halting. The input of the Busy Beaver function is the number of these things, which are denoted Q in the definition of a DFA.
ANSWER: states [or automaton states]
[10h] The equivalence arises from the DPRM theorem, which asserts that functions with this property can be written as Diophantine equations. Languages with this property are type 0 in Chomsky’s hierarchy, opposite regular languages at type 3.
ANSWER: recursively enumerable [reject “recursive”]
<MY, Other Science>
Summary
| Florida | 2025-02-01 | Y | 3 | 10.00 | 67% | 33% | 0% |
| Great Lakes | 2025-02-01 | Y | 6 | 6.67 | 50% | 17% | 0% |
| Lower Mid-Atlantic | 2025-02-01 | Y | 6 | 10.00 | 67% | 33% | 0% |
| Midwest | 2025-02-01 | Y | 6 | 13.33 | 83% | 50% | 0% |
| North | 2025-02-01 | Y | 3 | 16.67 | 67% | 100% | 0% |
| Northeast | 2025-02-01 | Y | 5 | 10.00 | 80% | 20% | 0% |
| Overflow | 2025-02-01 | Y | 5 | 10.00 | 60% | 40% | 0% |
| Pacific Northwest | 2025-02-01 | Y | 2 | 5.00 | 50% | 0% | 0% |
| South Central | 2025-02-01 | Y | 2 | 20.00 | 100% | 100% | 0% |
| Southeast | 2025-02-01 | Y | 4 | 2.50 | 25% | 0% | 0% |
| UK | 2025-02-01 | Y | 10 | 14.00 | 90% | 50% | 0% |
| Upper Mid-Atlantic | 2025-02-01 | Y | 8 | 10.00 | 75% | 25% | 0% |
| Upstate NY | 2025-02-01 | Y | 3 | 6.67 | 33% | 33% | 0% |