Prove that twice of ten is the same as twice of eleven.

Write the next letter in this sequence.
O, T, T, F, F, S, S, E, __
**Hint: It is a Number Series Puzzle

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?

A research team went to a village somewhere between the jungles of Africa. Luckily for them, they reached the day when quite an interesting custom was to be performed. The custom was performed once a year as they confirmed and was performed in order to collect the taxes from every male of the region.

The taxes were to be paid in the form of grains. Everyone must pay pounds of grain equaling his respective age. This means a 20-year-old will have to pay 20 pounds of grain and a 30-year-old will pay 30 pounds of grain and so on.

The chief who collects the tax has 7 weights and a large 2-pan scale to weigh. But there is another custom that the chief can weigh only three of the seven weights.

Can you find out the weights of the seven weights? Also, what is the maximum age of the man that can be weighed for the payment of taxes?

Imagine you are in a room with no windows or doors. How will you get out?

A man wants to cross the pit of fire which is 25 feet in length and he has 2 planks(fire resistant) 19 feet in length. How can he cross the pit of fire alive?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

I have branches, but no fruit, trunk or leaves. What am I?

How many triangles can you find in this given picture?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?