Fewest Number of Moves Necessary for the Pinch Hitter - Honors Algebra
The dugout at the Central High School baseball field is shared by both the home team and the visiting team. There is a bench in the dugout for "pinch" hitters. The right side of the bench is designated for the pinch hitters of the team that is at bat. The left side of the bench is designated for the pinch hitters of the team that is in the field. The two teams are separated by one empty seat. When the teams at play change positions, the pinch hitters must also shift positions; the hitters on the left side must move to the right side and the hitters on the right side must move to the left side.
The long awaited game between rivals Central high and Dayton high was on Sunday. There were 4 pinch hitters from central and 6 pinch hitters from Dayton on the bench. Before the game, Coach Madden told the pinch hitters, "Follow my rules carefully so that you can make the switch in the fewest number of moves." What is the fewest number of moves necessary for the pinch hitters to make the switch?
1.) Only one player may move at a time
2.) A player initially on the left side may only move to the right and a player initally on the right side may only move to the left.
3.) A player, on his move, may pass in front of only one player of the OPPOSING team or move into an adjacent empty seat.