Question 22
Eleven distinct chemicals $C_1,C_2,\ldots,C_{11}$ are to be stored in three different warehouses. Each warehouse stores at least one chemical. A pair $\{C_i,C_j\}$ of chemicals, where $i\ne j$, is either compatible or incompatible. Any two incompatible chemicals cannot be stored in the same warehouse. However, a pair of compatible chemicals may or may not be stored in the same warehouse. Find the maximum possible number of pairs of incompatible chemicals that can be found among the stored chemicals.