Determine the number of stereoisomers of 2,7-dibromoocta-3,5-diene, $\mathrm{CH}{}_3-\mathrm{CHBr}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CH}-\mathrm{CHBr}-\mathrm{CH}{}_3$. Count both stereocentres and both double bonds, treat each stereoisomer once, and note that the two halves are constitutionally identical (the molecule is symmetric about the midpoint of the C4-C5 bond). Give the answer as an integer.

There are four stereo-units: two stereocentres (C2 and C7) and two double bonds (C3=C4 and C5=C6), giving $2^4=16$ labelled combinations. The molecule maps onto itself when the two halves are exchanged, which swaps the labels of the two centres and of the two double bonds. Distinct molecules are the orbits under this exchange: 4 combinations are unchanged by it and the other 12 pair up, so $(16+4)/2=10$. The answer is 10.