Question
Finite groups with this property compose the 26 sporadic groups, the largest of which is the monster group. For 10 points each:
[10h] Name this property of groups that contain no non-trivial normal subgroups. The smallest non-Abelian group with this property is A5.
ANSWER: simple
[10m] McKay observed monstrous moonshine by connecting the monster group to this mathematician's j-invariant. This namesake of a "four-group" also names a non-orientable surface that is self-intersecting when embedded in 3D space.
ANSWER: Felix Klein [accept Klein bottle]
[10e] The fundamental polygon of the Klein bottle is this shape, whose symmetries compose the group D2. Matrices with equal numbers of rows and columns have this shape.
ANSWER: square (D2 is isomorphic to the Klein four-group.)
<Science - Other Science - Computer Science>
Data
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
|---|---|---|---|---|---|
| Adlai E. Stevenson A | Uni of Illinois Laboratory | 0 | 0 | 10 | 10 |
| Audrain County AT | Northview | 0 | 10 | 10 | 20 |
| Belmont | Innovation Academy A | 0 | 10 | 10 | 20 |
| Eastchester | Northmont | 0 | 0 | 10 | 10 |
| Fremd | Alabama Cyber Tech | 0 | 10 | 10 | 20 |
| Johns Creek | Richard Montgomery | 0 | 10 | 10 | 20 |
| Lexington | Detroit Catholic Central A | 0 | 0 | 10 | 10 |
| Lindbergh | Walter Payton A | 0 | 0 | 10 | 10 |
| Montgomery Blair A | Lambert A | 10 | 10 | 10 | 30 |
| Strake Jesuit A | Hunter A | 0 | 0 | 10 | 10 |
| Thomas Jefferson A | Strake Jesuit B | 0 | 0 | 10 | 10 |
| Westwood | Hinsdale Central A | 0 | 10 | 10 | 20 |
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2025 PACE NSC | 06/07/2025 | Y | 12 | 15.83 | 100% | 50% | 8% |