Question 22
Let $U$ be a set of $m$ triangles. Prove that there exists a subset $W$ of $U$ satisfying the following conditions.
(i) The number of triangles in $W$ is at least $0.45m^{4/5}$.
(ii) There exist no 6 distinct points $A, B, C, D, E$, and $F$ such that $W$ contains 6 triangles $ABC, BCD, CDE, DEF, EFA$, and $FAB$.
(i) The number of triangles in $W$ is at least $0.45m^{4/5}$.
(ii) There exist no 6 distinct points $A, B, C, D, E$, and $F$ such that $W$ contains 6 triangles $ABC, BCD, CDE, DEF, EFA$, and $FAB$.