The tertiary bromide shown is warmed in ethanol (no added base). Counting only constitutionally distinct neutral organic products formed through the carbocation (the substitution product and every alkene from loss of a beta proton), how many products form?

The compound is 1-bromo-1-methylcyclohexane. The tertiary cation is trapped by ethanol to give 1-ethoxy-1-methylcyclohexane ($\mathrm{S}{}_{\mathrm{N}}1$). Loss of a ring beta proton gives 1-methylcyclohexene, and loss of a methyl proton gives methylenecyclohexane ($\mathrm{E}{}_1$). Total: 1 + 2 = 3 products.