tournament seeding

tournament_seeding.rb

teams = (1..16).to_a
# => [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] 
games = (0..7).inject([]){|g, i| g << [teams[i], teams[-i-1]] }
# => [[1, 16], [2, 15], [3, 14], [4, 13], [5, 12], [6, 11], [7, 10], [8, 9]] 
# so now, how do I transform that to:
# => [[1, 16], [8, 9], [5, 12], [4, 13], [6, 11], [3, 14], [7, 10], [2, 15]]
# In essence, I have the teams already sorted into the games of who plays who in this round.
# But I want to order the games so they appear next to who will play the winners of this round in the next round.