The stairs in the tower of Sheik Oil Well

Did you ever wonder why medieval sultans have such beautiful daughters? Or why they have such complicated ways to select their suns in law?

1) Sheik Oil Well^*
Sheik Oil Well had two huge towers in the middle of the desert. His oldest daughter was renowned for her beauty, and suitors for her fair hand came from all the neighbouring oases.
The sheik told them: Do you see the left tower? He who can tell me how many steps the stairs have, without going up and counting them, will win her hand. I will tell you this: the number of stairs is three more than a prime number. When you would run up with 5 steps at a time, you would find that your last jump would only be 4 steps. When you divide the number of steps by 7, you would have 5 left. Oh, and the number of steps is a multiple of 19.

What is the smallest possible number of steps?

You can check your solution at here

I wish you everything that is good for the new year!

Please try to solve the puzzles on your own. You are welcome to remark on the puzzles, and I love it when you comment variations, state wether they are too easy or too difficult, or simply your solution times. Please do not state the soultions – it spoils the fun for others. I usually make the solution available after one or two weeks through a link, which allows readers to check the solution without the temptation to scroll down a few lines before having a go at it themselves.

Cross out

1) Cross out 5×5^**
In the square below, cross out numbers until the sum is 15 in every row and column:

2) Cross out 7×7^**
In the following square, cross out numbers till you the sum is 15 in every row and column:

This type of puzzle was probably invented by Rita Hovestad or Marenke Wiersma, editors of Sanders Brainteaser no 5.

You can check your solution here for no 1 and here for no 2

A new puzzle is published every friday. The solution is generally published one week later. I welcome your reactions on these puzzles: are they too easy, too difficult, are trhere any multiple solutions? How long did you need to solve it?

Odd one out

1) Letters
A H I M N O V W X
Which letter is the odd one in this series? solution

2) Digits
0 3 6 7 8 9
Which digit does not belong in this series? solution

3) Numbers
3 4 7 13 20 33 53 86 139
Which number does not belong in this series? solution

4) Ells

Which L does not belong in this series? (solution)

5) Series
Which of the 4 series above is different from the rest? (solution)