proof - 2025 ACF Fall - Buzzpoints App

Question

Examples of programs that aid in accomplishing this task include Lean and Rocq. For 10 points each:

[10e] Name this mathematical task, which often ends with writing a black square or the initials Q. E. D. Methods of accomplishing this task include induction and contradiction.

ANSWER: proof [accept word forms such as proving]

[10h] This task was the subject of a famous computer-aided proof completed by Appel and Haken in 1976. The minimum number of values used in this task, symbolized chi, is equal to two for bipartite graphs.

ANSWER: coloring [accept graph coloring or map coloring; accept, but DO NOT OTHERWISE REVEAL, four color theorem; prompt on chromatic number]

[10m] In their proof, Appel and Haken proved that any map can be colored with at least this many colors so that no two adjacent regions share the same color. Abel and Ruffini proved that this is the largest degree of a polynomial for which there exists a method to solve using radicals.

ANSWER: four [accept four color theorem]

<Editors, Other Science>

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Summary


Northern California	Main	Y	4	22.50	100%	75%	50%
Southern California	Main	Y	7	25.71	100%	86%	71%
Eastern Canada (1)	Main	Y	5	20.00	100%	60%	40%
Eastern Canada (2)	Main	Y	9	18.89	89%	78%	22%
Florida	Main	Y	4	22.50	100%	100%	25%
Great Lakes	Main	Y	12	24.17	100%	92%	50%
Lower Mid-Atlantic	Main	Y	9	17.78	78%	78%	22%
Upper Mid-Atlantic	Main	Y	2	20.00	100%	50%	50%
Midwest	Main	Y	9	20.00	78%	78%	44%
North	Main	Y	4	25.00	100%	100%	50%
Northeast	Main	Y	10	25.00	100%	100%	50%
Pacific	Main	Y	8	23.75	88%	88%	63%
South Central	Main	Y	7	18.57	57%	100%	29%
Southeast	Main	Y	13	23.85	92%	92%	54%
UK (North)	UK	Y	5	24.00	100%	100%	40%
UK (South)	UK	Y	8	23.75	100%	100%	38%
Upstate NY	Main	Y	5	22.00	100%	80%	40%

Data


Berkeley Little Prince	Stanford A	10	0	10	20
Berkeley Archer Queen	Stanford B	10	10	10	30
Berkeley Boss Bandit	Berkeley Mighty Miner	10	10	10	30
UCSD A	UC Santa Barbara	10	10	10	30
UCLA A	USC A	10	0	10	20
UCLA C	UCSD B	10	10	10	30
UCLA E	USC B	10	0	0	10
Carleton A	Carleton B	10	10	10	30
McGill A	McGill B	10	10	10	30
Ottawa B	McGill C	10	0	0	10
Ottawa C	McGill E	10	0	0	10
Ottawa D	Ottawa A	10	0	10	20
McMaster B	Toronto E	10	0	10	20
McMaster C	Toronto I	10	0	10	20
Queen's A	Toronto F	10	10	10	30
Toronto A	Toronto C	10	0	0	10
McMaster A	Toronto B	10	0	10	20
Guelph A	Toronto G	10	0	10	20
Toronto H	Brock A	10	0	10	20
Waterloo A	Toronto D	10	10	10	30
Waterloo C	Waterloo B	0	0	0	0
Claremont A	Claremont B	10	10	10	30
UCLA D	UCLA B	10	10	10	30
UCLA F	UC Irvine	10	10	10	30
Berkeley Skeleton King	UCSC	10	0	0	10
Florida A	Florida B	10	10	10	30
Florida Tech B	ERAU Daytona A	10	0	10	20
Florida State A	South Florida A	10	0	10	20
UCF A	Florida Tech A	10	0	10	20
Michigan A	CWRU A	10	10	10	30
Louisville A	CWRU B	10	0	10	20
Ohio State B	CWRU D	10	10	10	30
Kentucky	Louisville D	10	0	10	20
Michigan State A	Michigan B	10	10	10	30
Louisville B	Michigan C	10	10	10	30
Ohio State A	Michigan State B	10	10	10	30
Ohio State C	CWRU C	10	0	10	20
Ohio State D	Louisville C	10	0	10	20
Michigan D	Pittsburgh	10	10	10	30
Michigan State C	WVU A	10	0	0	10
Michigan State D	WVU B	10	0	10	20
Liberty C	NCSU B	0	0	0	0
Liberty A	Duke A	10	0	10	20
JMU B	Liberty B	0	0	0	0
Virginia Tech C	UNC C	10	0	10	20
VCU A	UNC B	10	0	10	20
Virginia A	William & Mary A	10	10	10	30
Virginia Tech A	Virginia Tech B	10	0	10	20
William & Mary B	William & Mary C	10	0	10	20
Maryland A	George Mason A	10	10	10	30
Maryland C	Rutgers A	10	0	0	10
UNC A	NCSU A	10	10	10	30
Iowa A	Chicago A	10	0	0	10
Illinois Champaign	Illinois Blue	10	10	10	30
Indiana A	Illinois Canada	0	0	10	10
Purdue C	Purdue A	10	10	10	30
Purdue B	Iowa B	10	10	10	30
William Woods University A	Rose-Hulman A	10	0	10	20
WashU Grizzlers	Indiana B	10	0	10	20
Purdue D	WashU Grolars	0	0	0	0
Chicago B	Illinois Urbana	10	10	10	30
Iowa State	Macalester	10	10	10	30
Michigan Tech	Wisconsin B	10	0	10	20
St. Thomas	Wisconsin A	10	10	10	30
Wisconsin C	Minnesota	10	0	10	20
Amherst B	Tufts C	10	0	10	20
MIT A	Boston College A	10	10	10	30
Boston University A	Brandeis Bach	10	0	10	20
Amherst A	Brown A	10	10	10	30
Dartmouth B	Brown B	10	0	10	20
Vermont B	Dartmouth A	10	10	10	30
Harvard	Williams C	10	0	10	20
Brandeis Beethoven	MIT B	10	0	10	20
Tufts B	UConn A	10	10	10	30
Brandeis Mozart	Williams B	10	10	10	30
Arizona State B	Washington Coho	10	10	10	30
Washington Steelhead	Alberta A	10	10	10	30
Washington State	Arizona State A	10	10	10	30
British Columbia A	Texas	10	10	10	30
Washington Atlantic	British Columbia B	10	0	10	20
Washington Chum	British Columbia C	10	10	10	30
Washington Pink	Washington Sockeye	10	0	10	20
Boise State	Washington Masu	0	0	0	0
Central Oklahoma B	Kansas State A	0	0	10	10
Rose State	Kansas State B	10	0	10	20
Murray State College B	Nebraska C	0	0	10	10
Nebraska B	Central Oklahoma A	10	0	10	20
Oklahoma	Murray State College A	0	0	10	10
Nebraska A	Tulsa A	10	10	10	30
Tulsa B	Harding	10	10	10	30
Auburn A	Auburn B	10	0	10	20
Mississippi State A	Auburn C	10	0	0	10
Alabama A	Chipola College	0	0	10	10
Clemson B	Clemson C	10	0	10	20
Georgia A	Tennessee Tech	10	0	10	20
Georgia Tech F	Georgia Tech B	10	10	10	30
Clemson A	Georgia Tech C	10	10	10	30
Georgia Tech D	Montevallo	10	10	10	30
Emory A	Georgia Tech E	10	10	10	30
Vanderbilt A	South Carolina A	10	10	10	30
Georgia Tech A	Tennessee A	10	10	10	30
Sewanne	Tennessee B	10	0	10	20
Vanderbilt B	Vanderbilt C	10	10	10	30
Durham D	Edinburgh B	10	10	10	30
Durham A	Edinburgh A	10	10	10	30
Edinburgh C	Durham C	10	0	10	20
York	Edinburgh D	10	0	10	20
Sheffield A	Durham B	10	0	10	20
Cambridge D	Bristol	10	10	10	30
Imperial B	Cambridge C	10	10	10	30
Cardiff	Cambridge B	10	0	10	20
Warwick	Imperial A	10	0	10	20
Imperial C	LSE	10	0	10	20
Cambridge E	Imperial D	10	0	10	20
Cambridge A	Oxford	10	10	10	30
Cornell B	Binghamton C	10	0	10	20
Cornell A	ESF	10	10	0	20
RIT B	Cornell D	10	0	10	20
RIT A	Cornell C	10	10	10	30
Rochester	Binghamton B	10	0	10	20
Southampton	Birmingham	10	0	10	20