This is the editorial for the Unofficial Div 4 Round #2 created by SlavicG and mesanu.

We hope everyone had fun and enjoyed the contest!

Problem A — Catching the Impostor.

Problem B — Epic Permutation

Problem C — Similar Arrays

Problem D — Sanda's Job

Problem E — Count Substrings

Problem F — Game on Grid

If n = 0 (mod2) then you can split the grid into sections of squares with 4 smaller squares each, wherever Bob colours he will at most nullify 4 squares. If n = 2 (Mod 4) then if Bob always plays correct(nullifying 4 squares every moves) Alice still wins because they will play for an odd number of moves.

If n = 0 (mod 4) then then Bob's strategy is to just eliminate one colour. Because Alice needs all colours present to move the game will end in $$$\frac{n^2}{8}$$$ moves, this number being even so because playing optimally they can at most get 4 squares each move each will get the same number of squares.

If n is odd, then Bob will focus on the colour that is least present ( even column, even row ). Alice will get $$$4\cdot(\lfloor\frac{(n-1)^2}{8}\rfloor+1)$$$ and Bob will get $$$4\cdot\lfloor\frac{(n-1)^2}{8}\rfloor + 2\cdot n-1$$$ so Bob will get more for $$$n \geq 3$$$.

Exception for $$$n = 1$$$ but its easy to see that Bob would win.