A word I know has six letters it contains, remove one letter and 12 remain. What is it?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

If EELS + MARK + BEST + WARY = EASY

What does HELP + BARK + WARD + LEAD equal?

A cat had three kittens: Snophy, Topsy and Jorden. What was the mother's name?

I ask Joseph to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Jack can't see any of this). I look at the cards and I pick 1 card out and give it back to Joseph. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Jack.

Jack looks at the 4 cards i gave him, and says out loud which card Joseph is holding (suit and number). How?

The solution uses pure logic, not sleight of hand. All Jack needs to know is the order of the cards and what is on their face, nothing more.

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

What kind of band never plays music?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

A man lives on the fifteenth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator, or if it was raining that day, he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up five flights of stairs to his apartment. Can you explain why he does this?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain