How can you divide a space of 22 people into 11 people 20 times?

 One way to divide a space of 22 people into 11 people 20 times is:

  1. Divide the 22 people into two groups of 11 people each.
  2. Choose 11 people from the first group and call them Group A1.
  3. Choose 11 people from the second group and call them Group B1.
  4. Combine Group A1 and Group B1 to create Space 1.
  5. Repeat steps 2-4, but this time choose a different set of 11 people from each of the two groups. Call these groups A2 and B2, and combine them to create Space 2.
  6. Repeat steps 2-5, choosing different sets of 11 people each time, until you have created 20 spaces.

Note that each person will be part of exactly two spaces.

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