I am quite hot but become too cold if you remove the first two letters. What am I?

Using the clues below, what four numbers am I thinking of?

The sum of all the numbers is 31.
One number is odd.
The highest number minus the lowest number is 7.
If you subtract the middle two numbers, it equals two.
There are no duplicate numbers.

What can go up a chimney down, but can’t go down a chimney up?

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

Replace the question mark with the number below given a simple math problem.

A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?

What is in seasons, seconds, centuries and minutes but not in decades, years or days?

What is the word or phrase?

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?