hey dudes my sister brought home a sheet of interesting maths puzzles she'd been given at school becasue its maths weeks here in ireland.

anyway one of them has me a bit confused!!

you have an "n" digit number
each digit can assume only one of 3 values 1,2,3,

so in this n digit number what percentage of the time do all 3 values (1,2,3) appear at least once!

best i can see is 2/9 of the time, regardless of the length of the number!! but i'm thinking this may be wrong, because if the number grows drastically to say a billion digits, and each digit can only be one two or three, then surely most of the time in this string of a billion digits 1,2,3 will appear and so the percentage should rise as the value n increases??
actually i'm 100% sure i'm wrong with my 2/9ths, i'll work on it a bit more and post again!!

i wont go through my workings just yet, i'd be interested to hear what others have to say