Here are 10 free mind games to exercise your brain:

1. Sudoku

About the game

SudokuSudoku is a logic-based number placement puzzle. The objective is to fill a 9×9 grid so that each column, each row, and each of the nine 3×3 boxes (also called blocks or regions) contains the digits from 1 to 9, only one time each (that is, exclusively). The puzzle setter provides a partially completed grid. (source)

Where to play

Resources

2. Chess

About the game

ChessChess is played on a square chequered chessboard with 64 squares arranged in an eight-by-eight square. At the start, each player (one controlling the white pieces, the other controlling the black pieces) controls sixteen pieces: one king, one queen, two rooks, two knights, two bishops, and eight pawns. The object of the game is to checkmate the opponent’s king, whereby the king is under immediate attack (in “check”) and there is no way to remove it from attack on the next move. (source)
For more information, see the rules of chess.

Where to play

Resources

3. Bridge

About the game

Bridge Contract bridge, usually known simply as bridge, is a trick-taking card game of skill and chance. It is played by four players who form two partnerships; the partners sit opposite each other at a table. The game consists of the auction (often called bidding) and play, after which the hand is scored. (source)
For more information, see the rules of bridge.

Where to play

These sites require you to log in and play against other human players. I couldn’t find free sites that allow you to play bridge online against computer.

Resources

4. Crossword

About the game

CrosswordA crossword is a word puzzle that normally takes the form of a square or rectangular grid of black and white squares. The goal is to fill the white squares with letters, forming words or phrases, by solving clues which lead to the answers. (source)

Where to play

Resources

5. Go

About the game

GoGo is played by two players alternately placing black and white stones on the vacant intersections of a line grid. The objective of the game is to control a larger part of the board than the opponent. (source)
For more information, see the rules of Go.

Where to play

Resources

6. Checkers

About the game

CheckersCheckers is a form of the draughts board game played on an 8×8 board with 12 pieces on each side that may only move and capture forward. (source)
For more information, see the rules of checkers.

Where to play

Resources

7. Reversi

About the game

ReversiReversi are names for a board game which involves play by two parties on an eight-by-eight square grid with pieces that have two distinct sides. The object of the game is to make your pieces constitute a majority of the pieces on the board at the end of the game, by turning over as many of your opponent’s pieces as possible. (source)
For more information, see the rules of Reversi.

Where to play

Resources

8. Connect Four

About the game

Connect FourConnect Four is a two-player board game in which the players take turns in dropping alternating colored discs into a seven-column, six-row vertically-suspended grid. The object of the game is to connect four singly-colored discs in a row — vertically, horizontally, or diagonally — before your opponent can do likewise. (source)

Where to play

Resources

9. Chinese Checkers

About the game

Chinese CheckersChinese checkers is a board game that can be played by two to six people. The objective of the game is to place one’s pieces in the corner opposite their starting position of a pitted 6-pointed star by single moves or jumps over other pieces. (source)
For more information, read the rules of Chinese checkers.

Where to play

Resources

10. Mastermind

About the game

MastermindMastermind is a simple code-breaking board game for two players (source). For more information, read the rules of Mastermind.

Where to play

Resource

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The ten games above are enough to improve your brain fitness. But, in case you got bored, there are plenty of other mind games you can find on these sites:

Whatever game you choose, play it and boost your brain’s performance.