Bean2

In each of these games there are beans which players take turns removing. The player to remove the last bean wins/loses. One of these games turns out to be pretty interesting.The game itself is very simple. You start with one or more lines of beans. On a players turn he may either remove an entire line of beans or remove a single bean, breaking a line into two lines (unless it was at the end of a line). The player to remove the last bean loses.For example, say we start with a single line of 3 beans. The legal moves are to remove all the beans (and immediately lose!), to remove an end bean (leaving a line of 2 beans) or remove the center bean (leaving two lines of 1 bean each). It`s not hard to see that the first player to move loses.