5 Challenging Math Games

At first glance, Nim seems as simple as tic-tac-toe, and can be played almost as quickly. In fact, the game is much more subtle and difficult. The play involves two players alternately taking away items from five piles containing one, two, three, four and five objects. The player who takes the last piece wins.

On a turn, a player must choose one pile from which to take pieces. He or she can take any number of pieces from that pile, but must take at least one piece. The key is to keep in mind how many pieces are in each pile, what your opponent's options are, and what the number in each pile might be several moves ahead. For example, you have to prevent your opponent from leaving you with only two piles with one piece in each. Planning and calculating are essential.

The name of this game comes from the German word for "take," and games similar to Nim have existed for centuries. A Harvard mathematician "solved" the game in 1901, calculating a perfect winning strategy using a binary number system. Even the earliest computers were able to play the game. It's claimed that a 1942 invention for playing Nim may be the oldest electronic game in existence.

Usually the game is played with five piles. You can use matches, coins or just marks on a piece of paper. Playing with different number of piles is also possible. And you can switch the whole game around so that the person who takes the last piece loses.

It sounds simple, but Nim strategy is very tricky. You'll find your head spinning with numbers as you try to take, and leave, the right number of items. There is no easy formula to guide you, just your feel for the game.

In 2004, Japanese educator Tetsuya Miyamoto invented a game he thought would help his students hone their math skills. He named it KenKen, a variation on ken, the Japanese word for wisdom. In 2008, Reader's Digest introduced the game to America, and The New York Times began to print versions of the game every day. Other newspapers followed suit, and the game became widely popular.

The goal of KenKen is to fill in a square grid with numbers. The key restriction is that no number can be repeated in a row or column. The squares range from 3 by 3 to 9 by 9, and the numbers used to fill in the grid are the same as the dimensions of the square. For example, a 5 by 5 square uses 1,2,3,4 and 5.

To some, this will sound very similar to another game popularized in Japan called Sudoku. But KenKen adds a twist. Within the square, certain cells are marked off by darker lines. The numbers inside these "cages" must, using an arithmetic function such as addition or division, produce a target number. The function and the target number are specified for each cage.

The game can be simple or hard depending on the size of the square and the design. Requiring a combination of simple arithmetic and complex logic, some large KenKen squares take hours to solve.

This classic game originated in ancient Egypt and later spread to Greece and Ireland. The Vikings also played it and took it to other parts of Europe. It's known by other names, including Mill, Merel and in French, Jeu de Moulin. Players can use a dedicated board to play or just sketch a simple diagram. During the Renaissance, Nine Men's Morris players sometimes marked out huge diagrams on plazas and used girls and boys as counters, ordering them where to move.

The board has 24 connected points that form three concentric squares, with lines connecting the squares' sides. Each player starts with nine stones or counters. Players alternate laying down stones at any points they choose. Once all are laid down, they move stones along the lines. The object is to form "mills," which means three stones in a row. Creating a mill allows the player to take one of the opponent's stones. One player wins when the other cannot move, or when his or her opponent has fewer than three stones remaining.

For young players, Nine Men's Morris offers practice in counting, adding and subtracting. Adults might appreciate the complex mathematics and computing power needed to "solve" the game, or in other words, determine a game plan that results in at least a draw. A good strategy in Nine Men's Morris is to spread your counters on the board. Try to set up a situation where you can open and close a mill repeatedly by moving a single stone. This allows you to keep taking your opponent's pieces.

The Internet is loaded with games to make math more interesting to learn. Most are aimed at students, and their purpose is to convince kids that math doesn't have to be boring and difficult but can be challenging and fun. The games come in many levels that correspond to how much math the player has learned.

"Math Blaster" is one of the most popular versions. In this Web-based computer game, the player is a recruit at Blaster Academy. He or she designs an avatar, then heads off on missions, interacting with other characters in outer space.

Achieving the game's objectives requires knowing and using math concepts. The player builds credits that increase his or her powers in the game by solving math equations. The idea is that kids are too busy having fun and zapping aliens to notice that they are also engaged in math drills. They can move to increasing levels of difficulty, from kindergarten to sixth grade, as their math skills improve.

"Math Blaster," developed by Knowledge Adventure, Inc., is free, though a paid membership offers more advanced levels and access to other games.

Mancala is the name for a group of games that are among the oldest in the world. They originated in Africa and are still widely played there, but Mancalalike games have spread as far as Central Asia and the Philippines. The name comes from the Arabic word for "transfer," and may have originated from devices for keeping merchants' accounts. The version in Ghana is known as Oware; in Kenya it's called Giuthi; in the Philippines they play Sungka. The rules vary by region, but the concept is always one of moving stones or seeds through a series of cups.

The setup for Mancala is an array of cups, usually 12 divided into two parallel rows, with a scoring pit for each of the two players at either end. Think of an egg carton, which can in fact be used to play the game. Each player puts four counters in each of the six cups on his or her side. The first player takes the counters from any cup and, moving counterclockwise, deposits one counter in each cup until they're gone. If the last counter is dropped into one of the opponent's cups and forms a group of two or three, those pieces can be captured and transferred to your scoring pit. The goal is to win the most counters.

The game gets interesting as you calculate not only your own move, but the number of pieces left in your cups and how your opponent might score on the next move. You have to do lot of fast counting.

The beauty of Mancala is that it can be played with an elegant board and glass beads or with pebbles or beans in hollows scooped in the dirt. Despite the simple layout, expert play is very difficult. The fact that it draws on complicated calculations, intuition and planning makes it one of the most challenging of all math games.