13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from the above-mixed cards to guarantee at least one 'four of a kind?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

A father told his three sons he would die soon and he needed to decide which one of them to give his property to. He said, “Go to the market and buy something large enough to fill my bedroom, but small enough to fit in your pocket. From this, I will decide which of you is the wisest and worthy enough to inherit my land.” They all went to the market, and each came back with a different item. The father told his sons to come into his bedroom one at a time and try to fill up his bedroom with their items. The first son came in and put some pieces of cloth he bought and laid them across the room, but it barely covered the floor. The second son came in and laid some hay on the floor, but there was only enough to cover half the floor. The third son came in and showed his father what he bought. He wound up getting the property. What did the third son show his father?

We are a group of eight brothers. We consider the weak, yet we protect the king in every battle. If we move ahead, we never turn back. Who are we?

An artist while painting a scenic beauty, decides to paint three layers of blue colour on the sky.

Which layer will go on the first?

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

Without looking at a calendar, within a minute name, a boy's name using 5 consecutive 1st letters of 5 consecutive months

An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

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?