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]
<Other Science>
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 |
| 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 |
| 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 |
| McGill E | Arkansas | 10 | 0 | 10 | 20 |
| Central Oklahoma | NYU A | 10 | 0 | 0 | 10 |
| Mississippi State | Vassar B | 0 | 0 | 0 | 0 |
| Missouri | Texas B | 0 | 0 | 10 | 10 |
| Ole Miss | WUSTL A | 10 | 0 | 0 | 10 |
| Texas A | NYU B | 10 | 10 | 10 | 30 |
| 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 |
| 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 |
| 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 |
| 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 |
| Texas D | Texas C | 0 | 0 | 0 | 0 |