Eggified - a maths strategy game

This is a simple game for two players. The focus is on logical deduction and strategic thinking.

The children pay on a board that consists of an 11-sided polygon (a hendecagon). They start the game by placing a counter on each of the eggs.

Then, they take it in turns to remove either 1 or 2 adjacent counters. The player who picks up the very last counter is the winner.

It is as simple as that!

encourage the children to play the game a few times to see what happens. There are some prompts on the board itself to help the children to identify a winning strategy. There is one... since this mathematical game is not totally fair!

The second player has an unfair advantage in the game. For example, imagine the first player chose to remove two counters, like this.

In order to force a win the second player needs to take a single counter on his turn. He also needs to choose a counter which is exactly opposite the first player's original selection.

Since players can only take away one or two adjacent counters on each turn, this breaks the chain of counters into two separate, but equal sections. The second player now follows whatever the first one does, clearing one side away at a time – they will find they can take the last counter, thereby winning.

Should the first player only take one counter on their initial go, then the second player takes two adjacent ones at the opposite side of the board – mirroring the first two goes of the earlier play. The result is the same. Consequently, the second player (with a little bit of concentration) can always win the game.

The game has some clear connections with the game of Nim.

The strategy fails if the board contains an equal number of starting points.

The one page pdf file attachment, below, contains a simple black and white game board, instructions and prompts to help the children think about developing a winning strategy.

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