Question
A theorem that inspired this field implies that, for a party with 6 people, there must be a group of 3 mutual acquaintances or a group of 3 mutual strangers. For 10 points each:
[10m] Name this field, whose key results include the Hales-Jewett theorem. This field is sometimes thought of as an extension of combinatorics.
ANSWER: Ramsey theory
[10e] More abstractly, Ramsey's theorem asserts the existence of a minimum number of vertices that guarantees the existence of monochromatic cliques in a “complete” one of these structures.
ANSWER: graphs
[10h] This major result in Ramsey theory states that, given two integers k and p, there is some number W such that coloring the first W natural numbers with k colors yields a color with an arithmetic progression with p terms. This theorem's namesake developed a way of using dotted or undotted indices to denote right or left-handed spinors.
ANSWER: van der Waerden's theorem [or van der Waerden notation or Bartel Leendert van der Waerden]
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Summary
| 2023 BHSU @ Berkeley | 03/18/2023 | Y | 3 | 16.67 | 100% | 33% | 33% |
| 2023 BHSU @ Maryland | 03/11/2023 | Y | 3 | 16.67 | 100% | 33% | 33% |
| 2023 BHSU @ Northwestern | 02/25/2023 | Y | 6 | 20.00 | 100% | 100% | 0% |
| 2023 BHSU Online | 04/15/2023 | Y | 4 | 17.50 | 100% | 75% | 0% |
| 2023 BHSU @ Sheffield | 04/15/2023 | Y | 2 | 15.00 | 100% | 50% | 0% |
| 2023 BHSU @ Waterloo | 04/15/2023 | Y | 3 | 16.67 | 100% | 67% | 0% |
| 2023 BHSU @ Yale | 04/08/2023 | Y | 3 | 16.67 | 100% | 67% | 0% |
Data
| Cornell B- | Cornell C++ | 10 | 10 | 0 | 20 |
| Dr. Christopher Manners, MD – Samarra, Iraq | Rollin in from Sturgis, The Cheyne Gang | 10 | 10 | 0 | 20 |
| Houston and friends | What is BH! And you are asking me? BHSU | 0 | 10 | 0 | 10 |
| Hutto Hippos | The Enrique Trastamara Military Academy B | 10 | 10 | 0 | 20 |