Question 26
Each of the numbers from $100$ to $999$ inclusive is written on a separate card. The cards are arranged in a pile in random order. We take cards off the pile one at a time and stack them into $10$ piles according to the last digit. We then put the $1$ pile on top of the $0$ pile, the $2$ pile on top of the $1$ pile and so on to get a single pile. We now take them off one at a time and stack them into $10$ piles according to the middle digit. We then consolidate the piles as before. We then take them off one at a time and stack them into $10$ piles according to the first digit and finally consolidate the piles as before. What can we say about the order in the final pile?