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Puzzles based on games

This section focuses on the best behavior strategies in various known (and not very) board games. Also here are all puzzles based on games, for example interesting chess problems.

1) Double chess.
Two play chess according to the following rules: first they make two moves white, then two moves are black, then again two moves are white, etc. If one of the kings is declared a shah (dopystim, chechnomy), then in this case, the creep moves to the black, but they have the right only one turn to get away from the shah (if you can not go one turn, then, as usual, .)
The task: to prove that in such a white with the best game is guaranteed as a minimum draw. Answer

2) On the normal chessboard is a white korol (field A1), and a black box (field D4). Add two white rooks and a white horse so that the black root is corroded. 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 board sized N * N so that they do not threaten each other? Answer

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

6) Put it last.
On an ordinary chessboard, two players take turns to place checkers (alternatively, cigarettes) so that they do not come in contact with 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 to put on a chess board so that each cell is under attack? (Different elephants and / or rooks can stand on cells of the same color) Answer

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

9) Here is the task: to place on the chess board a minimum number of rooks so that each field is attacked no less than 2 rooks. The rook can attack through another rook and does not attack the field on which it stands. 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 (Alternatively, the cards) and in turn the opponents take 1, 2 or 3 matches. Who takes the last - lost. Is there any strategy for the correct game? Answer

11) In the classical tetris 7 figures are used:

  [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] [] []
  [] [] [] [] [] [] [] [] [] 
Is it possible to use the following set of figures to construct the following figures:
1. rectangle 4 * 7
  [] [] [] [] [] [] []
 [] [] [] [] [] [] []
 [] [] [] [] [] [] []
 [] [] [] [] [] [] []
  2. triangle
 [] []
 [] [] []
 [] [] [] []
 [] [] [] [] []
 [] [] [] [] [] []
 [] [] [] [] [] [] [] 

12) There are 7 holes in a certain place. There are 6 pebbles in them, as depicted on a picture (three black ones and three white ones)

For each move, one of the following operations can be performed:
1. Move the pebble to the adjacent free hole
2. Move the pebble into a free hole which is located behind its immediate neighbor (crossing the neighboring pebbles)
What is the smallest number of moves you can change the places of black and white pebbles? Produce the appropriate sequence of moves. Answer

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

14) I suspect that everybody can play in a "fool". Here is the problem relating to this ancient and wise game: one player has a trump card on his hands, and the other has the rest of the deck and the right of the first move. Who wins with the best game of both sides? Answer