Draw the structures of the nine isomeric heptanes `(C_7H_(16))`.
Strategy: start with the straight chain isomer (longest chain). Going to a six-carbon chain, a `CH_3` may be placed either on `C-2` or on `C-3` to give two isomers. Starting with a five-carbon chain, either two `CH_3`, or a `CH_3CH_2` must be added as side chain for a total of seven C's. The two `CH_3` may be placed on the same C atom or on different carbons giving a total of four isomers. The `CH_3CH_2` group can only be placed on the central C atom. At other points it either lengtherns the chain or reproduces previous isomer.Finally, go for a four carbon chain and three `CH_3`'s to form the ninth isomer.

Explanation

`underset("Heptane")(CH_(3)CH_(2)CH_(2)CH_(2)CH_(2)CH_(2)CH_(3))" "underset(2-"Methylhexane")(CH_(3)overset(CH_(3))overset(|)(C)HCH_(2)CH_(2)CH_(2)CH_(3))`
`underset(3-"Methylhexane")(CH_(3)CH_(2)overset(CH_(3))overset(|)(C)HCH_(2)CH_(2)CH_(3))" "underset(2,2-"Demethylpentane")(CH_(3)underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)CH_(2)CH_(2)CH_(3))`
`underset(3,3-"Dimethylpentane")(CH_(3)CH_(2)underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)CH_(2)CH_(3))" "underset(2,3-"Demethylpentane")(CH_(3)overset(CH)overset(|)(C)Hunderset(CH_(3))underset(|)(C)HCH_(2)CH_(3))`
`underset(2,4-"Dimethylpentane")(CH_(3)overset(CH_(3))overset(|)(C)HCH_(2)underset(CH_(3))underset(|)(C)HCH_(3))" "underset(3-"Ethylpentane")(CH_(3)CH_(2)underset(CH_(3))underset(|)underset(CH_(2))underset(|)(C)HCH_(2)CH_(3))`
`underset(2,2,3-"Trimethylbutane")(CH_(3)underset(CH_(3))underset(|)overset(CH_(3))overset(|)(C)-underset(CH_(3))underset(|)(C)HCH_(3))`