Going from separate to alternating:
PPPPBBBB.. P..PBBBBPP PBBP..BBPP PBBPBPB..P ..BPBPBPBP
Back to Pick A Pair of Packets.
To get from the pattern of N P's followed by N B's to the pattern of N pairs of B's and P's takes N steps, but to reach the pattern of N pairs of P's followed by B's takes N+1 steps!