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.