Solution:

3

Explanation:
1 + 2 + 3 + 4 + 5 => 15 => 5 - 1 =>4
4 + 5 + 6 + 7 + 8 => 30 => 3 - 0 =>3
6 + 7 + 8 + 9 + 11 => 41 => 4- 1 =>3

Solution:

1

Explanation:
Because I have only one mouse and not a pair required for reproduction.

Solution:

The prisoner picks a marble and without showing it to anyone swallows it and then picks the remaining marble and shows to everyone which was black which proved the first marble prisoner pick must be white.
The Mad King has no option but to let the prisoner go.

Solution:

Fishing Net

Solution:

6

Explanation:
Key1: 3 attempts for 3 gates.
Key2: 2 attempts for remaining 2 gates.
Key3: 1 attempts for the last gate.

Solution:

A Party

Solution:

It can be done as shown below.

Solution:

11

Explanation:
Tzu‑ying won 3 games
V.Sindhu must win 3(to balance 3 games she lost) + 5 games(required for min 50$) = 8 games
Total Games = 3 + 8 = 11 games.

Solution:

A Clock

Solution:

The poison was not in pills but in water.