A particular computer game involves the capturing of three types of mythical creatures: Arps, Orps and Urps. Arps have 6 legs, 3 horns and a tail. Orps have 4 legs and 2 horns, but no tail. Urps have 3 legs and a tail, but no horns. The last time Billy played this game he captured 45 creatures with a total of 222 legs, 99 horns and 33 tails.