11 3 2 ooxxxoxxxoo
6 Takahashi is going to work on $3$ days out of the $11$ days. After working for a day, he will refrain from working on the subsequent $2$ days. There are four possible choices for his workdays: Day $1,6,10$, Day $1,6,11$, Day $2,6,10$, and Day $2,6,11$. Thus, he is bound to work on Day $6$.
5 2 3 ooxoo
1 5 There is only one possible choice for his workdays: Day $1,5$.
5 1 0 ooooo
There may be no days on which he is bound to work.
16 4 3 ooxxoxoxxxoxoxxo
11 16
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