Step 1: Approach Brown-Sequard by tracking three tracts through a one-sided cord lesion: the lateral corticospinal tract (motor), the dorsal column (fine touch, proprioception) and the spinothalamic tract (pain, temperature).
Step 2: Pain and temperature fibres synapse and decussate almost immediately after entering the cord. So a lesion on one side interrupts fibres that have crossed from the opposite side, producing contralateral loss of pain and temperature a couple of segments below the level. This crossed pain loss is the signature finding, so the contralateral pain-loss option is correct.
Step 3: Dismiss the alternatives. Proprioception and vibration travel in the ipsilateral dorsal column until the medulla, so their loss is on the same side as the lesion, not contralateral. Voluntary motor power is carried by the already-decussated corticospinal tract, so weakness is ipsilateral. There is no pure one-sided total sensory loss; the deficits dissociate across the midline.
\[\boxed{\text{Contralateral loss of pain (and temperature)}}\]