Unoficial Div 4 Round #2 Editorial

Revision en4, by SlavicG, 2020-11-16 17:37:59

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.

Tutorial

Problem B — Epic Permutation

Tutorial

Problem C — Similar Arrays

Tutorial

Problem D — Sanda's Job

Tutorial

Problem E — Count Substrings

Tutorial

Problem F — Game on Grid

Tutorial

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 n28 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((n1)28+1) and Bob will get 4(n1)28+2n1 so Bob will get more for n3.

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

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en18 English SlavicG 2020-11-26 23:09:03 84 Tiny change: ' Editorial for the problems](https://' -> ' Editorial](https://'
en17 English SlavicG 2020-11-26 00:41:29 1
en16 English mesanu 2020-11-25 23:05:22 884
en15 English SlavicG 2020-11-25 19:56:56 510
en14 English SlavicG 2020-11-25 19:51:53 116
en13 English SlavicG 2020-11-25 19:48:14 323 Tiny change: 'wing.\n\n<a href="https://ibb.co/fQsCdCZ%22%3E<img src="' -> 'wing.\n\n<img src="' (published)
en12 English SlavicG 2020-11-25 19:26:32 116 Tiny change: 'is problem\n\nProble' -> 'is problem.\n\nProble'
en11 English mesanu 2020-11-25 19:18:38 691
en10 English mesanu 2020-11-25 19:07:51 72 Reverted to en8
en9 English SlavicG 2020-11-25 18:58:37 72
en8 English SlavicG 2020-11-25 18:55:25 30 Tiny change: ' can find cases dep' -> ' can find the answer by looking at the cases dep'
en7 English SlavicG 2020-11-25 18:50:43 2638 Tiny change: 'from $1$. Let \textit{even cell} denote a ' -> 'from $1$. _Let even cell_ denote a '
en6 English SlavicG 2020-11-16 19:56:56 21 Tiny change: ' larger then the medi' -> ' larger than the medi'
en5 English SlavicG 2020-11-16 18:58:06 9199 Tiny change: '$ $2$ $=$ 0 it is a d' -> '$ $2$ $=$ $0$ it is a d'
en4 English SlavicG 2020-11-16 17:37:59 1142
en3 English SlavicG 2020-10-30 12:45:45 31 Tiny change: ' it would change by $x$.\nThe sam' -> ' it would become greater.\nThe sam'
en2 English mesanu 2020-10-30 00:56:04 912
en1 English SlavicG 2020-10-30 00:43:10 2525 Initial revision (saved to drafts)