A Storyteller’s Tale Many years ago, wandering storytellers travelled from village to village telling stories in exchange for food, shelter, and money. In some instances, their story telling skills were underappreciated…therefore they had to find another way (legally) to receive food and shelter. Some of these storytellers would go to the local restaurant and challenge villagers to a game of skill. If the storyteller won, the villagers would buy him dinner. If the storyteller lost, he would have to stay in the village and perform a variety of chores.

A Storyteller’s Tale The game itself seems simple. 20 beans are placed on a table. Two players take turns removing between 1 and 4 beans from the pile. The person who takes the last bean(s) wins. The wandering storytellers depended on winning this game to ensure they could receive a good meal when their storytelling skills were less than exemplary. Therefore, the storytellers had to devise a strategy to ensure they always won. Imagine you were a storyteller during this time period…what would your winning strategy be?

A Basic Set of Rules Start with a pile of 20 beans. One player may take 1 to 4 beans from the pile (the beans selected should be moved away from the original pile). The second player then takes 1 to 4 beans from the pile and moves the beans away from the original pile. Players alternate turns (taking 1 to 4 beans from the pile) until all the beans are removed. The player who is able to take the last bean (or beans) from the pile is declared the winner.

A Winning Strategy Play the game with a partner and devise a “winning” strategy. Make sure that your strategy will guarantee that you will win…and not go hungry!

Additional Considerations Is it important to be the first or second player? Does the number of beans removed by the other player influence how many beans you will remove? Does playing the game with fewer beans in the pile (5, 8 or 13, for example) help to influence your strategy?

The Strategy, Revealed! Draw, bullet or diagram a strategy for taking the last bean(s) of the original game (20 beans, each player takes between 1 and 4 beans). Make sure to: (1) Clearly communicate the strategy so that a person who has never played the game before can follow the strategy to victory, and (2) Explain why the strategy will always win (no matter what the other player does).

Other Games… How would your strategy change if the following were to occur: 23 beans were used instead of 20 beans (each person still takes 1 to 4 beans)? 31 beans were used and each player takes 1 to 5 beans? 47 beans were used and each player takes between 3 and 6 beans?

The Strategy, Revealed (part 2) Revise your previous strategy to provide a winning strategy for one of the three new games. Again, make sure the strategy clearly communicates how to win, and why the strategy works.