What occurs twice in a week, once in a year but never in a day?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

John was driving a bus and got stuck when passing through an underpass. Then came Jacob with a needle and got the bus out of the underpass.

What did the boy do?

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

A thief enters a store and threatens the clerk, forcing her to open the safe. The clerk says, “The code for the safe is different every day, and if you hurt me you’ll never get the code.” But the thief manages to guess the code on his own. How did he do it?

A pond had 60 fish, out of which, all but 20 died.
How many fishes are now present in that pond?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

If,
29 - 1 = 30
9 - 1 = 10
14 - 1 = 15

Based on similar logic, Can you prove that the below algebraic equation is true?
11 - 1 = 10 ?

A man stands on one side of a river, his dog on the other. The man calls his dog, who immediately crosses the river without getting wet and without using a bridge or a boat. How did the dog do it?