Packet 9: Bonus 3
Simulations that popularized this theory were conducted by Marc Davis, George Efstathiou, Carlos Frenk, and Simon White, who made up Berkeley’s “Gang of Four.” For 10 points each:
[10h] What theory describes a component whose “w” parameter is approximately zero? This theory predicts bottom-up structure formation.
ANSWER: cold dark matter [or CDM; prompt on Lambda-CDM by asking “what part of that theory?”; prompt on particle dark matter; reject “dark matter” alone]
[10e] The Gang of Four’s cosmological simulations treated structure formation as an instance of this problem. Poincaré proved that this problem cannot be analytically solved for three or more objects.
ANSWER: N-body problem [reject “many-body problem”]
[10m] Frenk, White, and Julian Navarro developed an analytical “profile” of this quantity through N-body simulations of galaxies. The first Friedmann equation implies that this quantity’s “critical” form equals 3 H squared over 8 pi G.
ANSWER: density [accept density profile; accept critical density]
<FW, Other Science (Astronomy)> | NAFTA-Packet-9
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 42 | 11.90 | 74% | 36% | 10% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Maybe Ever | WashU | 0 | 10 | 0 | 10 | E |
| St. Marx | [Redacted] | 0 | 0 | 0 | 0 | |
| The Worst Trade Deal in the History of Trade Deals | Lex | 0 | 10 | 10 | 20 | EM |
| four high school generalists shock natives with fluent stock in Tocharian B | W&L+Friend | 0 | 0 | 0 | 0 |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| 2026 NAFTA at Stanford | 01/17/2026 | ✓ | 4 | 12.50 | 75% | 50% | 0% |
| 2026 NAFTA at UBC | 01/17/2026 | ✓ | 2 | 0.00 | 0% | 0% | 0% |
| 2025 NAFTA Online | 02/14/2026 | ✓ | 4 | 7.50 | 50% | 25% | 0% |
| 2026 NAFTA at Vanderbilt | 02/14/2026 | ✓ | 3 | 20.00 | 67% | 67% | 67% |
| 2025 NAFTA at Toronto | 09/13/2025 | ✓ | 5 | 12.00 | 100% | 20% | 0% |
| 2025 NAFTA at Maryland | 09/27/2025 | ✓ | 5 | 16.00 | 60% | 60% | 40% |
| 2025 NAFTA at Harvard | 10/04/2025 | ✓ | 3 | 10.00 | 100% | 0% | 0% |
| 2025 NAFTA at Oxford | 10/11/2025 | ✓ | 3 | 13.33 | 100% | 33% | 0% |
| 2025 NAFTA at Chicago | 11/08/2025 | ✓ | 6 | 15.00 | 83% | 67% | 0% |
| 2025 NAFTA at Columbia | 11/08/2025 | ✓ | 5 | 10.00 | 80% | 20% | 0% |
| 2025 NAFTA at Richmond | 12/20/2025 | ✓ | 2 | 5.00 | 50% | 0% | 0% |