Numerical answer type, tolerance 0.5.
Answer: 5
The alcohol is 3,3-dimethylpentan-2-ol. The unrearranged secondary cation loses only a C-1 hydrogen, giving 3,3-dimethylpent-1-ene (1). The methyl shift gives the tertiary 2,3-dimethylpent-3-yl cation, which gives 2,3-dimethylpent-2-ene (1), (E)- and (Z)-3,4-dimethylpent-2-ene (2) and 2,3-dimethylpent-1-ene (1). The total is 1 + 1 + 2 + 1 = 5.