Quick and dirty method:

1) Get 35 cards, set aside 3.
2) Divide the 32 cards into 2 stacks of 16.
3) Number each stack with this binary sequence:
0000
0001
0010
0011
0100
...
1111
4) Number the remaining 3 cards 0000, 0001, 0010 (this is somewhat arbitrary).
5) Hand out the cards.
6) On the first day the teams will be comprised of the people with numbers ending with the same two digits. There will be four teams: 00, 01, 10 and 11.
7) On the second day people with the first digit of 1 will move to the adjacent team.
8) On the third day people with the second digit of 1 will move to the adjacent team.
9) On the fourth day people with the third digit of 1 will move to the adjacent team.

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