Why is 6 afraid of 7?

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

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

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

Suppose that you are trapped on the surface of a frozen lake. The surface is so smooth and ideal that there is no friction at all. You cant make any grip on the ice and no wind is blowing to help you out. You have just a mobile phone with you which has got no reception disabling you to call for help.

How will you plan your escape before you freeze to death on the frozen lake?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

You are provided with a grid (as shown in the picture). Can you fill the squares with numbers 1-8 in a manner that none of the two consecutive numbers are placed next to each other in any direction (vertically, horizontally or diagonally?)

What has hands, but can’t clap?

Consider all the numbers between 1 and 1 million. Among all these numbers, there is something very special about the number 8 and the number 2202. What is it?