Combing hair involves brushing away the topological tangles in a collective curl, defined as a bundle of
interacting elastic filaments. Using a combination of experiment and computation, we study this
problem that naturally links topology, geometry and mechanics. Observations show that the dominant
interactions in hair are those of a two-body nature, corresponding to a braided homochiral double helix.
This minimal model allows us to study the detangling of an elastic double helix driven by a single stiff
tine that moves along it and leaves two untangled filaments in its wake. Our results quantify how the
mechanics of detangling correlates with the dynamics of a topological quantity, the link density, that
propagates ahead of the tine and flows out the free end as a link current. This in turn provides a
measure of the maximum characteristic length of a single combing stroke in the many-body problem
on a head of hair, producing an optimal combing strategy that balances trade-offs between comfort,
efficiency and speed of combing in hair curls of varying geometrical and topological complexity.