What is more useful when it is broken?

Decode below rebus
D
N
A
T
S , D

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

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?

Can you count the number of triangles in the given picture?

What is the word or phrase?

There are two dice with empty faces in front of you and a marker. You can mark any number on each of the faces of the two dice, but you have to display all 31 days of the month using the two of them.

Which numbers will you mark on which dice so that you can easily depict all the dates of the month?

Count the number of balls in picture below:

In the image below, you can see two glasses and two matchsticks.You need to move four matchsticks in such a manner that the crosses come inside the glasses. Note: you cannot move the crossed.

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?