April 2021 - Solution
For n = 20, there are two sets with n-7 = 13 elements that are unwinnable:
(1, 2, 3, 4, 5, 6, 7, 8, 11, 14, 15, 16, 17) (4, 5, 6, 7, 10, 13, 14, 15, 16, 17, 18, 19, 20)
For n = 21, there are many sets with n-8 = 13 elements that are unwinnable. For example:
(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15)