If we interchange cards 6 and 13 and begin our count at 14, we may take
up all the twenty-one cards--that is, make twenty-one "catches"--in the
following order: 6, 8, 13, 2, 10, 1, 11, 4, 14, 3, 5, 7, 21, 12, 15, 20,
9, 16, 18, 17, 19. We may also exchange 10 and 14 and start at 16, or
exchange 6 and 8 and start at 19.