SQUARE GAME. All players have 4 counters and put one anywhere on the top row of the gameboard. Players throw the die in turn, using the Square Game key-table to find out where to go next, then move their counter on the top row, and record their first visit to a square by putting another of their other counters in the column below that position. They may visit the same top square many times, but they only record their first visit to each position. The winner is the first one to record a visit to all 4 squares, recording the  winning visit to the last square with the mover counter.

Notice the patterns of cycles 1234 in the square table.

The Rectangle Group game is played in the same way using the Rectangle key-table. Recording visits by putting counters in columns is visually more effective than a written record, but players can use a single strip of 4 squares and record their first visit to each square in their own way. The Triangle and Hexagon Games for 6 elements are played in a similar way.

The ways elements are combined determines the sequences of moves in the games. This is the main feature of these Groups Games. Otherwise the rules in the four games are the same. Notice the patterns of cycles 1234 in the Square Group Game table and cycles of 123456 in the Hexagon Group Game.

This is a new game invented, by Alan and Toni Beardon, published by Tarquin in the book Let’s Play Mathematically AIMSSEC Family Games.