What's the only room from which no one can enter or leave

You order chicken wings at KFC in the boxes of 6, 9 and 20. What is the largest number of wings that you cannot obtain by buying in any combination of the boxes?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

A prisoner is told: "If you tell a lie, we will hang you and if you tell the truth, we will shoot you." What did the prisoner say to save himself?

There is a circular car race track of 10km. There are two cars, Car A and Car B. And they are at the exact opposite end to each other. At Time T(0), Both cars move toward each other at a constant speed of 100 m/seconds. As we know both cars are at the same speed they will always be the exact opposite to each other.
Note, at the center, there is a bug which starts flying towards Car A at time T(0). When the bug reaches car B, it turns back and starts moving towards the car A. The speed of bug is 1m/second. After 5 hours all three stop moving.
What is the total distance covered by the bug?

Different lights make me strange by changing me into different sizes. What am I?

Two friends were stuck in a cottage. They had nothing to do and thus they started playing cards. Suddenly the power went off and Friend 1 inverted the position of 15 cards in the normal deck of 52 cards and shuffled it. Now he asked Friend 2 to divide the cards into two piles (need not be equal) with equal number of cards facing up. The room was quite dark and Friend 2 could not see the cards. He thinks for a while and then divides the cards in two piles.

On checking, the count of cards facing up is same in both the piles. How could Friend 2 have done it ?

Your job is to measure 45 minutes if you have only two cords and matches to light the cords.

1. The two cords are twisted from various materials, so their different segments can burn at different rates.
2. Each cord burns from end to end in exactly one hour.

Describe your way of measuring the 45 minutes.

Can you find out what is missing?

1 3 5
2 4 ?

Hint: It's not six. Think out of the box.