why number 8549176320 is one of a kind?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

John was writing his first book. After saving the document, he locked his laptop with a password and mentioned some phrases for the hint box.

A friend of his tried opening his laptop but found out that it was password protected. Following is the hint that appeared.
1 mobile 3 books 2 roars 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches.

Can you help him in cracking the password?

Prove that twice of ten is the same as twice of eleven.

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?

What does the below rebus puzzle mean?

My first is in chocolate but not in ham. My second is in cake and also in jam. My third at tea time is easily found. Altogether, this is a friend who is often around. What is it?

Can you find the ages of a son, father and grandfather based on the following facts?
The sum of the ages of grandfather, father and son is 140 years.
The age of the son in months is the same as the grandfather in years.
The age of the son in days is the same as the father in weeks.

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going toward the river. Each monkey had 1 parrot in each hand. How many animals are going towards the river?