You have a 12 liters jug full of water. You have two empty 8 liters and 5 liters jug. How can you divide the water into two equal parts using these jugs?

Prove that the below maths equation is true.

8 + 8 = 91

I never stop running even when I standstill. If I am formed by joining two identical bodies together, can you guess who I am?

I am quite hot but become too cold if you remove the first two letters. What am I?

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 ?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

What am I?