The Dimes and Quarters

Strategies and Hints

  1. Marking the coins gives you a way to record the moves and allows you to better keep track of what you are doing.

  2. The two possible moves from the goal position are to take the third dime and first quarter and to move them either to the left or the right of the row.

  3. Here are two solutions to the problem described in the fourth hint. In each move, the pair must touch a coin. A minimum of five moves is needed to solve this variation of the problem.

    1 A 2 B 3 1 A 2 B 3
    1 A · · 3 2 B 2 B 3 1 A
    3 2 B 1 A 3 1 A 2 B
    3 · · 1 A 2 B 3 · · 2 B 1 A
    3 A 2 1 · · B 3 B 1 2 · · A
    2 1 3 A B 1 2 3 B A

Solution

Here are four different solutions of four moves each.

1 A 2 B 3 1 A 2 B 3
1 A· ·3 · · · 2 B 2 B 3 · · · 1 A
3 · · 1 A 2 B 3 · · 2 B 1 A
3 A 2 1 · · B 3 B 1 2 · · A
2 1 3 A B 1 2 3 B A
   
1 A 2 B 3 1 A 2 B 3
1 A · · 3 · · 2 B 2 B 3 · · 1 A
3 · · 2 B 1 A 3 · · 1 A 2 B
3 B 1 2 · · A 3 A 2 1 · · B
1 2 3 B A 2 1 3 A B