Packet 9: Bonus 11
Examples of programs that aid in accomplishing this task include Lean and Rocq. For 10 points each:
[10e] Name this mathematical task, which often ends with writing a black square or the initials Q. E. D. Methods of accomplishing this task include induction and contradiction.
ANSWER: proof [accept word forms such as proving]
[10h] This task was the subject of a famous computer-aided proof completed by Appel and Haken in 1976. The minimum number of values used in this task, symbolized chi, is equal to two for bipartite graphs.
ANSWER: coloring [accept graph coloring or map coloring; accept, but DO NOT OTHERWISE REVEAL, four color theorem; prompt on chromatic number]
[10m] In their proof, Appel and Haken proved that any map can be colored with at least this many colors so that no two adjacent regions share the same color. Abel and Ruffini proved that this is the largest degree of a polynomial for which there exists a method to solve using radicals.
ANSWER: four [accept four color theorem]
<Editors, Other Science> | Packet I
| Editions | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|
| 2 | 121 | 22.31 | 92% | 88% | 44% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Claremont A | Claremont B | 10 | 10 | 10 | 30 | EHM |
| UCLA A | USC A | 10 | 0 | 10 | 20 | EM |
| UCLA C | UCSD B | 10 | 10 | 10 | 30 | EHM |
| UCLA D | UCLA B | 10 | 10 | 10 | 30 | EHM |
| UCLA E | USC B | 10 | 0 | 0 | 10 | E |
| UCLA F | UC Irvine | 10 | 10 | 10 | 30 | EHM |
| UCSD A | UC Santa Barbara | 10 | 10 | 10 | 30 | EHM |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| UK (North) | UK | Y | 5 | 24.00 | 100% | 100% | 40% |
| UK (South) | UK | Y | 8 | 23.75 | 100% | 100% | 38% |
| Northern California | US | Y | 4 | 22.50 | 100% | 75% | 50% |
| Southern California | US | Y | 7 | 25.71 | 100% | 86% | 71% |
| Eastern Canada (1) | US | Y | 5 | 20.00 | 100% | 60% | 40% |
| Eastern Canada (2) | US | Y | 9 | 18.89 | 89% | 78% | 22% |
| Florida | US | Y | 4 | 22.50 | 100% | 100% | 25% |
| Great Lakes | US | Y | 12 | 24.17 | 100% | 92% | 50% |
| Lower Mid-Atlantic | US | Y | 9 | 17.78 | 78% | 78% | 22% |
| Upper Mid-Atlantic | US | Y | 2 | 20.00 | 100% | 50% | 50% |
| Midwest | US | Y | 9 | 20.00 | 78% | 78% | 44% |
| North | US | Y | 4 | 25.00 | 100% | 100% | 50% |
| Northeast | US | Y | 10 | 25.00 | 100% | 100% | 50% |
| Pacific | US | Y | 8 | 23.75 | 88% | 88% | 63% |
| South Central | US | Y | 7 | 18.57 | 57% | 100% | 29% |
| Southeast | US | Y | 13 | 23.85 | 92% | 92% | 54% |
| Upstate NY | US | Y | 5 | 22.00 | 100% | 80% | 40% |