Ramsey numbers - 2024 PLAYTIME

Question

One of these numbers with indices (5, 5) is currently bounded between 43 and 48. For 10 points each:

[10h] Give these numbers named after an American mathematician. For indices m and n, this number is the smallest size of a two-colored complete graph such that there is always a monochromatic complete graph of size m or n.

ANSWER: Ramsey numbers

[10e] Ramsey theory is used to analyze social networks to determine how many people must know each other, with each relationship represented by coloring one of these things. These entities connect vertices on a graph.

ANSWER: edges [accept links or lines]

[10m] This “wandering” mathematician quipped that if aliens demanded the Ramsey number (6, 6), then humans should attack. His namesake “number” counts an author’s separation from him by collaboration on math papers.

ANSWER: Paul Erdős [or Erdős Pál; accept Erdős number]

<KP, Other Science - Math>

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Summary


2025 PLAYTIME @ CWRU	12/10/2024	Y	5	16.00	100%	60%	0%
2025 PLAYTIME @ Claremont	12/10/2024	Y	5	26.00	100%	100%	60%
2025 PLAYTIME @ Florida	12/10/2024	Y	2	25.00	100%	100%	50%
2025 PLAYTIME @ Florida	12/10/2024	Y	1	30.00	100%	100%	100%
2024 PLAYTIME @ Harvard	04/26/2025	Y	4	15.00	100%	25%	25%
2024 PLAYTIME @ JHU	10/26/2024	Y	8	16.25	88%	63%	13%
2025 PLAYTIME @ Northwest	12/10/2024	Y	4	22.50	100%	100%	25%
2025 PLAYTIME Online	04/26/2025	Y	9	20.00	78%	100%	22%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	6	18.33	100%	67%	17%
2025 PLAYTIME @ Sheffield	12/10/2024	Y	1	30.00	100%	100%	100%
2024 PLAYTIME @ UBC	10/05/2024	Y	8	22.50	88%	88%	50%
2024 PLAYTIME @ Virginia Tech	07/11/2025	Y	3	20.00	67%	100%	33%
2024 PLAYTIME @ WashU	10/12/2024	Y	6	15.00	83%	50%	17%

Data


Michigan A	Michigan B	0	10	10	20
Michigan C	Michigan D	0	10	0	10
Pittsburgh	Oberlin	0	10	10	20
Ohio State A	Ohio State B	0	10	10	20
Ohio State D	Ohio State C	0	10	0	10
UCLA B	UCLA A	0	10	10	20
Art of Premature Signaling	Caltech	10	10	10	30
Claremont A	Claremont B	10	10	10	30
UCSD	UCSB	10	10	10	30
girl 15 whale i mean they	P.C.‚ Daniel‚ Michel‚ and Jason B	0	10	10	20
Billy's Bastion	Qin Shi Huang's Immortality Poison	10	10	10	30
Edwin Laundrorat's Long-Lost Man Unclothès Rat Degrosses	Too much from you lately	0	10	10	20
Belmont	BU	0	10	0	10
Brandeis	Harvard	0	10	0	10
Lexington	Brown	0	10	0	10
MIT	RIT	10	10	10	30
Project2025BC: Make Assyria Great Again	Keeping Up With the Cardassians	10	10	10	30
CWRU	Johns Hopkins A	0	10	0	10
NYU B	George Washington	0	10	10	20
Haverford B	Johns Hopkins B	0	10	0	10
Georgetown	Maryland A	0	10	10	20
Maryland B	NYU C	0	10	10	20
Rutgers	Haverford A	10	10	10	30
Arizona State University B	South Dakota School of Mines	10	10	10	30
Alberta	UW A	0	10	10	20
Washington Connections	Arizona State University A	0	10	10	20
UW B	Carleton	0	10	10	20
George Mason A	George Mason C	0	10	10	20
2 Italians, 2 Poles, All Noles	mongeese	0	0	10	10
Free Agents 1	Egypt Airlines Haters	10	10	10	30
Four Generalists in Search of a Power	Illinois Orange	0	10	10	20
Goober Gang	MSJ	0	10	10	20
Auburn 2026	Gruh	0	10	10	20
Mahjonng Masters	we need new names	0	10	10	20
Quatumvirate	Notre Dame + Epic Games	0	10	10	20
Mike Dukakis Tank Battalion	Trip-Hop Quizzer Tricky	10	10	10	30
evil women enjoyers	Monsieur Hulot's Academic Team	0	0	10	10
Sheffield A	Sheffield B	10	10	10	30
Imperial B	Birmingham	0	10	0	10
Cambridge	Warwick B	10	10	10	30
LSE	Imperial A	0	10	10	20
Manchester	Sheffield C	0	10	10	20
Lancaster	Warwick A	0	10	0	10
Warwick C	Edinburgh	0	10	10	20
McGill A	Ottawa A	10	10	10	30
Toronto A	Toronto D	10	10	10	30
Toronto B	Guelph	0	10	10	20
George Mason B	Catholic University of America	0	0	0	0
Toronto C	McGill B	10	10	10	30
Toronto Metropolitan	Toronto E	0	10	0	10
Simon Fraser	UBC	0	10	10	20
Waterloo A	Mac A	10	10	10	30
Waterloo C	Waterloo B	0	0	10	10
Ashurbanipal’s Drag Race	4 quizbowl pros go Virginia on North Carolina	0	0	10	10
Even in Blacksburg There I Am	Adrianne Lenker 4 Nobel Lit Prize 2K65	10	10	10	30
Somehow Paula Deen Returned	Master and Margaritaville	0	10	10	20
Chicago B	Illinois C	0	10	10	20
Missouri	Illinois A	0	0	0	0
Chicago A	Iowa State	10	10	10	30
SIUE	WashU Squirtle	0	10	0	10
WashU Bulbasaur	Truman State	0	10	10	20
Illinois B	WashU Charmander	0	10	0	10