What is more useful when it is broken?

How many sides does a circle have?

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?

There is a jar in which there are two types of candies.
20 blueberries and 16 strawberries. You perform the following steps:
1) You take out two candies.
2) If the two candies are of the same flavour, you add a blueberry one otherwise, you add the strawberry one.

You repeat these two steps till there is just one candy remaining in the jar. Which flavoured candy will be left?

What is black when you buy it, red when you use it, and gray when you throw it away?

Forwards I am heavy, backward I am not. What am I?

Spot the cat in the picture below

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?