Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

In a university, a professor gave a set of three problems to the three brilliant students of his class. See the image for the questions.

Solve the alphametic puzzle by replacing the alphabet with the number.

S T O R M +
S O L E S
=========
T O W E L
=========

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

You are given with the following sum. Each of the letters can be decoded as a digit. If we tell you that D = 5, then can you solve it entirely?

DONALD
+GERALD
=ROBERT

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

Akbar called Birbal and asked him to draw a line on the floor. He asked Birbal to make that line smaller without erasing it. Birbal smiled and did it before Akbar could blink his eyes.

How did he managed to do it?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

Can you find out the remainder when 3^300 is divided by 5?

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?