I look at you, you look at me I raise my right, you raise your left. What am I?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

Below is the sum of symbols in each row and column in the figure. Analyzing the figure, can you find out the value of the symbols?

Can you find the key in the picture below?

What's a single-digit number with no value?

What demands an answer, but asks no questions

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.

The product of three consecutive numbers is 7980.
Then the sum of these consecutive numbers would be?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?