Riemann hypothesis - 2025 ACF Regionals

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>

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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%

Data


Florida State A	Florida B	10	0	10
Florida A	UCF B	10	10	20
Valencia A	UCF C	0	0	0
Carnegie Mellon A	Case Western B	10	0	10
Case Western A	Michigan B	0	0	0
Michigan State	Kenyon	0	0	0
Michigan A	Carnegie Mellon B	10	0	10
Michigan C	Michigan D	10	10	20
Ohio State B	Ohio State A	0	0	0
Duke	Wake Forest	10	10	20
Liberty C	Liberty A	0	0	0
Virginia Tech A	Liberty B	10	0	10
UNC C	South Carolina	0	0	0
UNC D	UNC B	10	10	20
Virginia A	William & Mary	10	0	10
Chicago B	Chicago D	10	0	10
Chicago A	Chicago C	10	10	20
Illinois B	Missoui S&T	10	10	20
Indiana A	Illinois C	10	10	20
WashU B	WashU A	0	0	0
Iowa State	Wisconsin B	10	10	20
Minnesota B	Wisconsin A	0	10	10
Winona State	Carleton	10	10	20
Dartmouth A	BU	10	0	10
Brandeis B	Tufts A	0	0	0
Brandeis A	Brown A	10	10	20
Harvard A	MIT A	10	0	10
Harvard B	UMass Boston	10	0	10
Georgetown A	Notre Dame B	0	0	0
Notre Dame A	Georgetown B	0	0	0
Northwestern B	Iowa	10	0	10
Purdue	Northwestern A	10	10	20
Stanford B	Notre Dame C	10	10	20
Alberta	UW B	0	0	0
UW A	UBC	10	0	10
Illinois A	Missouri	10	0	10
TAMU	Texas B	10	10	20
Alabama A	Georgia Tech A	0	0	0
Louisville A	Georgia Tech D	0	0	0
Georgia Tech B	Tennessee A	10	0	10
Georgia Tech C	Vanderbilt A	0	0	0
Texas A	ASU	10	10	20
Bristol	Southampton A	10	10	20
Cambridge A	Southampton B	10	10	20
Cambridge C	Durham	10	0	10
Imperial B	Cambridge B	10	0	10
LSE	Warwick B	10	0	10
Manchester	Oxford B	10	0	10
NYU C	Cambridge E	0	0	0
Oxford A	Sheffield	10	10	20
Cambridge D	Oxford C	10	10	20
Imperial A	Warwick A	10	10	20
Rutgers A	Cornell B	10	0	10
George Washington A	Columbia C	0	0	0
George Washington B	Maryland A	0	0	0
Vassar A	Haverford A	10	0	10
Haverford B	Penn B	10	0	10
John Jay College	Columbia B	10	10	20
NYU A	Penn A	10	10	20
Yale A	Johns Hopkins A	10	0	10
ESF A	Cornell C	0	0	0
RIT A	Binghamton A	10	10	20
Cornell D	RIT B	0	0	0