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Game based puzzles

This section is devoted to the best strategies for behavior in various well-known (and not so) board games. Also here are all the puzzles based on games, for example interesting chess problems.

1) Double chess.
Two play chess according to the following rules: first make two moves white, then two moves black, then again two moves white, etc. If one of the kings is declared a check (let's say black), then in this case the move immediately goes to black, but they have the right only one move to leave the check (if it is impossible to leave in one move, then, as usual, checkmate .)
Objective: to prove that in such a game, white with the best game is guaranteed as a minimum draw. Answer

2) On a regular chessboard there is a white king (field A1), and a black king (field D4). Add two white rooks and a white horse so that the black king is matted. Answer

3) How many horses do you need to attack the whole board? To control the whole board? Answer

4) What is the maximum number of horses that can be placed on a N * N sized board so that they do not threaten each other? Answer

5) How many queens (queens) do you need to attack the entire chessboard? Answer

6) Put last.
On a regular chessboard, two players take turns putting checkers (cigarettes as an option) so that they do not touch each other. The goal is to put your checker last. Is there a winning / win-win strategy? Answer

7) What is the minimum number of pieces you need to put on a chessboard so that each cell is under attack? (Different bishops and / or rooks can stand on the same color cells) Answer

8) What is the maximum number of queens that can be placed on a chessboard so that they do not attack each other? On a n * n sized board? Answer

9) This is the task: to place the minimum number of rooks on the chessboard so that each field is attacked by no less than 2 rooks. A rook can attack through another rook and does not attack the field it stands on. Answer

10) A simple (and most common) version of the game "him":
Probably everyone knows the game, where several matches are put on the table (as an option, cards) and, in turn, opponents pick up 1, 2 or 3 matches. Who takes the last - lost. Is there any strategy for the right game? Answer

11) In the classic tetris 7 figures are used:

  [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] []
  [] [] [] [] [] [] [] [] [] 
Is it possible using one set of such figures to build the following figures:
1. 4 * 7 rectangle
  [] [] [] [] [] [] []
 [] [] [] [] [] [] []
 [] [] [] [] [] [] []
 [] [] [] [] [] [] []
 [] []
 [] [] []
 [] [] [] []
 [] [] [] [] []
 [] [] [] [] [] []
 [] [] [] [] [] [] [] 

12) In some place there are 7 holes. There are 6 pebbles in them, as shown in the figure (three black and three white)

For each move, you can perform one of the following operations:
1. Move the pebbles to the adjacent free hole
2. Move the pebble to a free hole which is located behind its immediate neighbor (jumping over the next pebble)
What is the smallest number of moves that you can swap black and white pebbles in? Conduct the appropriate sequence of moves. Answer

13) I think you all know how chess pieces are arranged and how they go? Here's a riddle for you: playing on both sides, for what minimum number of moves from the beginning of the game you can checkmate one of the parties, and what kind of moves they will be. By the way, this year I put just such a mat, playing with the enemy. But he plays poorly. I played 50 games with him and won everything. Answer

14) I suspect that everyone knows how to play the “fool”. Here is the problem related to this ancient and wise game: one player has a trump card, and the other has the rest of the deck and the right of the first move. Who wins the best game on both sides? Answer