Riddles, brain puzzles and mathematical problems

[MyRedNeptune]

@BAndrew

Thank you! So you're not fazed by the last step of my solution? That's mainly what I was referring to when I mentioned lousy technique.

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

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

Spoiler below!

This is totally easy. To start, write down your digit of choice. This will be the "moving digit" and the first digit of the number m. Let's call it a. Multiply a by 2 and write the first digit of the result in the space to the left of it, adding any applicable 1's in the process. Repeat the process with the resulting new digit.

Keep doing this until two conditions are met:

-the leftmost digit is 1/2*a (if a is even) or 1/2*(a-1) (if a is odd)
-if a is even, the second leftmost digit times two gives a single-digit number; if a is odd, the second leftmost digit times two gives a double-digit number

This will lend us the smallest possible m for any a. Multiply by 2 to get n.

@Chrono Sorry, probability is... I just forgot everything. :S