Solution:

1 * 1 = 1
11 * 11 = 121
111 * 111 = 12321
1111 * 1111 = 1234321


Following the pattern, you can come straight at:
111111111 * 111111111 = 11=2345678987654321

Solution:

Anybody will prefer the shop in the eastern market for sure. There are two reasons for it:
Firstly, since there are only two barbers in the town, the one running the shop in eastern market must have gotten his hair done by the one running the shop in the northern market and vice versa. Thus, if the barber in the eastern market has a shabby haircut, it must be due to the incompatibility.
Secondly, the neat and clean shop can be due to the scarcity of customers as well. While the untidy place refers to the fact that so many customers get their hair done in that shop.

Thus any one will opt for the barber shop in the eastern market.

Solution:

White should move the rook from
A1 to D1 and hence complete the castling move.

Solution:

40

Solution:

None

The sum of numbers from 0-9(0,1,2,3,4,5,6,7,8,9) is 45 and therefore can be divisible by 3 and 9.

Solution:

Four

three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.

Solution:

The Letter 'A' is silent in the parliament.

Solution:

Draw a tilted line on 1st plus (+) operator, + will become 4 :-)
The equation then becomes true: 545+5=550.

Solution:

888+88+8+8+8=1000

Solution:

18

Explanation:
More minutes implies more tea.
More women implies more tea.

The time become twice (3 minutes / 1.5 minutes).
women become six times (9 / 1.5).

Number of tea = 2 * 6 * Original(1.5)
= 18