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% |
Data
| 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 |