The Puzzle Corner this week has two versions which are variations of a common theme in manipulation puzzles. In each game the goal is to switch the position of two or more sets of coins by moving them within the spaces provided. Coins may only move into adjacent empty spaces. No jumping is allowed, but coins may move in either direction.
In Version One there is a row of 13 squares, with two additional squares above the middle square. In this version, four pennies are placed at the four far-left squares, and four dimes are placed in the four far-right squares. The challenge is to switch the positions of the dimes and the pennies, and to do this in the fewest possible moves. Coins may be moved by sliding them into an empty space adjacent to the one they are in. Coins may move in either direction, but you may not jump coins at any time.
Once you have solved the puzzle, attempt to do it in the fewest possible moves. Describe your solution.
In Version Two there are two rows of 11 squares connected by a single square in the middle. Version Two has two games, both of which require four types of coins. Quarters go in the upper left corner, nickels go in the lower left corner, dimes go in the upper right corner, and pennies go in the lower right corner.
Use quarters, nickels, dimes and pennies. Place four quarters in the upper left squares, four nickels in the lower left squares, four dimes in the upper right squares, and four pennies in the lower right squares. The object is to have the quarters and nickels trade places and the dimes and pennies trade places. The same rules apply as before, coins may move into any adjacent empty space, and no jumping is allowed.
Set up the board the same as in game one, only this time the challenge is to switch the quarters and the pennies and then switch the dimes and the nickels.
You may decide to use both or only one of these versions with your students.
Other objects may be substituted for coins, however, they must be small enough to fit in the spaces on the student sheets, and be of four different types. Colored buttons, different types of beans, centicubes would all work equally well.
Click the arrow below to view the solution.
Students were challenged to switch the position of coins in various arrays using the fewest number of moves each time. For the sake of simplicity, one move is considered to be any time a coin moves, regardless of the number of spaces it moves.
In version one, the pennies and dimes can be made to switch places in 20 moves.
In version two, both games can be solved in a total of 44 moves – 22 moves to switch each set of coins.
If you or your students are able to solve any of the versions in Coin Capers in a fewer number of moves, please send us a description of your solution(s) in the comment section below.