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To seat all the 1001 guests, then tables of size of the factors of 1001 will do:

The 8 factors of 1001, and thus the possible table sizes, are: 1, 7, 11, 13, 77, 91, 143, 1001

So you could have:

1001 tables with 1 seat each

143 tables with 7 seats each

91 tables with 11 seats each

77 tables with 13 seats each

13 tables with 77 seats each

11 tables with 91 seats each

7 tables with 143 seats each

1 table with 1001 seats

100 tables that seat ten (leave 1 guest unseated)

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Q: How many possible table sizes that will seat an equal number of guest for 1001 guest?
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