Chapter 11, Problem 11.55P

Devise a synthesis of the ketone, $\text{hex}-3-\text{one}$, ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{\text{COCH}}_{\text{2}}{\text{CH}}_{\text{2}}{\text{CH}}_{\text{3}}$ from ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}\text{Br}$ as the only organic starting material. You may use any other needed reagents.