There are $10$ hunters who are planning to go hunting in as a few days as possible. Every single day, they choose a group of people or a person to go for hunting, the rest is resting in the camp area. Next day, they choose again who is/are going to go for hunting etc. But they want to make sure of three things at the end of the hunting;
- Any hunter would go for hunting without any other hunter in the group for at least one day. For example, if hunter $A$ goes with hunter $B$ for a day, hunter $A$ should go for a hunting at least one more time without hunter $B$, same goes for hunter $B$ of course etc.
- As a group of 10 people, they want to go hunting as few days as possible.
- Every hunter needs to go for hunting at least for a day.
So what is the least number of days is needed for hunters to complete hunting with the condition above?
If this question was asked for 3 people, the answer would be $3$ such as below;