up arrows - 2024 ACF Winter

Question

The incredibly large Graham’s number can be expressed by using 64 recursive layers of these symbols between 3 and 3 in one notation. For 10 points each:

[10m] Name these symbols. Donald Knuth introduced a notation in which one of these symbols put between two numbers denotes exponentiation, while two of them denote tetration.

ANSWER: up arrows [accept equivalents mentioning arrows pointing upwards or caret; accept Knuth’s up-arrow notation; prompt on arrows]

[10h] Graham’s number was introduced as an upper bound for a graph coloring problem in this field of math. Van der Waerden’s theorem and the Hales–Jewett theorem are two main results in this branch of combinatorics.

ANSWER: Ramsey theory

[10e] Graham’s number cannot be directly represented by the chained arrow notation that this mathematician introduced to express very large numbers. He also developed a cellular automaton called his “Game of Life.”

ANSWER: John Conway [accept Conway’s Game of Life]

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Summary


2024 ACF Winter at UC Berkeley	2024-11-16	Y	3	23.33	100%	100%	33%
2024 ACF Winter at Lehigh	2024-11-16	Y	6	10.00	50%	50%	0%
2024 ACF Winter at Northwestern	2024-11-16	Y	9	17.78	78%	78%	22%
2024 ACF Winter at Ohio State	2024-11-16	Y	7	15.71	86%	71%	0%
2024 ACF Winter at Online	2024-11-16	Y	8	12.50	50%	63%	13%
2024 ACF Winter at UBC	2024-11-16	Y	3	23.33	100%	100%	33%
2024 ACF Winter at Central Florida	2024-11-16	Y	5	14.00	60%	80%	0%
2024 ACF Winter at Oxford	2024-11-16	Y	11	21.82	100%	91%	27%
2024 ACF Winter at Brandeis	2024-11-16	Y	10	14.00	60%	60%	20%

Data


Berkeley A	Berkeley C	10	10	10	30
Berkeley B	Stanford A	10	0	10	20
Stanford M	Stanford L	10	0	10	20
McGill E	Arkansas	10	0	10	20
Central Oklahoma	NYU A	10	0	0	10
Mississippi State	Vassar B	0	0	0	0
Boston University B	A Brandeis Supreme	0	0	0	0
Williams A	Amherst A	0	0	0	0
Yale B	Bowdoin A	10	0	10	20
Brown A	Carabrandeis	10	10	10	30
Notre Dame	WashU D	0	0	10	10
UIUC B	Purdue A	10	0	10	20
Indiana B	Purdue D	0	0	0	0
UChicago B	SIUE A	10	0	0	10
UIUC D	UChicago D	10	0	10	20
Indiana A	UIUC A	10	10	10	30
UChicago A	UIUC C	10	0	10	20
WashU B	UChicago C	10	10	10	30
Northwestern A	WashU C	10	0	10	20
CWRU B (UG)	CWRU D (DII)	10	0	10	20
Kenyon B (DII)	Michigan C (UG)	0	0	0	0
Michigan State B (UG)	Kenyon A (UG)	10	0	10	20
CWRU A (UG)	Michigan State C (UG)	10	0	10	20
Pitt B (UG)	Ohio State B (DII)	10	0	10	20
Michigan B	Ohio State C (DII)	0	0	10	10
Pitt A	Michigan D	10	0	10	20
Birmingham	Oxford B	10	0	10	20
Imperial A	Bristol B	10	0	10	20
Cambridge B	Southampton B	10	10	10	30
Cambridge D	Durham B	10	10	10	30
Edinburgh	Durham A	10	0	10	20
Imperial B	Warwick B	10	0	10	20
LSE B	Cambridge C	10	0	10	20
LSE A	Southampton A	10	0	10	20
Southampton A	Southampton B	10	0	10	20
Oxford A	Team 1	10	10	10	30
Bristol A	Warwick A	0	0	10	10
Bard A	Columbia B	0	0	10	10
Haverford A	Rowan A	0	0	0	0
Columbia A	Johns Hopkins A	10	0	10	20
Penn State B	Penn B	10	0	0	10
Penn State A	Penn A	0	0	10	10
Lehigh A	Rutgers C	10	0	0	10
Missouri	Texas B	0	0	10	10
Ole Miss	WUSTL A	10	0	0	10
Texas A	NYU B	10	10	10	30
Texas D	Texas C	0	0	0	0
Oregon State	Vassar A	10	0	10	20
UBC A	UW B	10	0	10	20
Alberta	UBC B	10	0	10	20
SFU	UW A	10	10	10	30
UCF B	Florida State University A	0	0	0	0
UF A	UF B	10	0	10	20
UCF A	UF C	10	0	10	20
UF D	Florida Tech B	10	0	10	20
Florida Tech A	UF E	10	0	0	10
Bowdoin B	Clark A	10	0	10	20
Diamond Brandeis	Boston University A	0	0	0	0
Brandeises Brew	Harvard A	0	0	0	0
MIT A	Northeastern A	10	0	10	20
Yale A	Tufts B	10	10	10	30
Tufts A	Yale C	10	0	10	20