2. A 13-digit display shows the number 1201201201201. Robots C3PO and R2D2 take turns rearranging its digits. In one move, they can swap two adjacent digits, but it is forbidden to swap digits on positions that have already been swapped by either robot. Additionally, a zero cannot be placed in the first position. The player who cannot make a move loses. Who will win with correct play if C3PO starts?
Solution. C3PO will win. It is enough for him to swap the first zero with the two on his first move. After this, in any case, 10 more moves will be made - one can freely perform permutations in all pairs of adjacent positions, except for the 2nd and 3rd (which have already been swapped) and the 1st and 2nd (swapping which will result in placing a zero at the beginning).