Riddles, brain puzzles and mathematical problems

[BAndrew]

@MyRedNeptune

So you're not fazed by the last step of my solution?

No.

Hm, today I found another solution to the same problem. This one takes like 5 minutes, and it's more elegant.

Well done again!

I'm quite curious what your solution is, too.

My solution is more similar to your second solution, but instead of multiplying I use division. It is a bit hard to describe though. So I will use some pictures to illustrate the steps.

Pick up a digit (I picked up 9 because why not) and then you devide it with 2 using long division.

We know that the number n must be divisible by 2 exactly. We start to do division normally. So in my case the first step is this:



Because we put the first digit (the 9 in this case) in the end we know that 4 is the second digit of the number n.



Then 7 must be the third digit for the same reason.



Continue to do this until both of the following conditions are met:

• The last digit in the quotient is a 9 (or the digit you began with)
  
• The remainder is 0
  

Then you have your number!

I am actually too lazy to continue the process but you can see that it works. The number I found was 18 digits long or something like that, but I lost the paper I have written it down. It doesn't take more than 5 minutes to find it though.

@Froze
OK Froze we got it, probabilities are your Jesus. Every problem you've posted so far has probabilities in it. I don't have anything against probabilities, but I know only the basics or even less about the subject.

EDIT:

I'll post a new problem either today 21:00-22:00 GMT or tomorrow the same time.

There is also Froge's riddle if anyone wants to try.