NIM
One of the oldest math puzzle games is NIM. This two-player game begins with anywhere from five to 10 markers (such as chips or coins) on the table. Each player takes a turn, with the option of removing one to two markers from the table. The object is to force your opponent to take the last chip, thereby losing the game. The strategy here is to think ahead several moves, always assuming your opponent will make the best move possible.
Sudoku
The game board for this numbers puzzle is a 3x3 grid of boxes. Each of these boxes also has a smaller 3x3 grid inside it. The boxes will contain the numbers one through nine once, in some order, in the nine squares. The numbers one through nine will also appear once, in some order, in each row of the entire game board and each column of the entire game board.
Each puzzle is initially set up with some of the numbers filled in and the rest of the squares left empty. The goal is to fill in the empty squares using the provided numbers as clues. To solve the puzzle, determine the possible number in each square by looking at numbers already used in that square's box, row and column. It's easiest to complete the puzzle by starting with squares that only have a few possibilities left. A common strategy is to make small marks within each square to keep track of possible solutions for that square until the correct answer is obtained.
Peg Solitaire
This math puzzle is designed for one person and is available as a peg game (pegs on a wooden board) or a marble game (also on a wooden board, but with marbles). Every hole on the board except one is filled with a peg. The game is played by jumping pegs and removing the jumped peg from the board. The goal is to jump pegs in such a way that at the end of the game, only one peg is left. This requires thinking ahead and planning so no peg gets isolated and stuck on the board without any way to jump or be jumped.