Well this question from the Russian mathematical olympiad (I am interested in this question because of its level to solve)
2 friends Tom and Peter play a game as follows: Peter read to Tom writes the numbers from 1 to 8 (each number is written once) in the order that Peter wants. Tom writes them down on a piece of paper, adding each digit, Starting from the 2nd number, write to the left or right of all the given numbers written. The result on a piece of paper has a 9-digit number. Tom wants the number to be written down as large as possible, Peter wants it to be as small as possible. Ask for the number what is the gain if both play very well.