# CHALLENGE

The Puzzle of the 7 Coins!!!

The object of this puzzle is to place a coin on all the vertices but one of the star in Figure 1 (shown with smaller dimensions).

When placing any coin, you should move it along a free line, and put it down at the end of that line.  A line is called free if there is no coin at either of its endpoints.  The numbers at the vertices are to help you explain your strategies according to the six-step MathWorld Interactive problem-solving format.

Three coins in a puzzle...

Three dimes (the small circles in Figure 4 below) and two quarters (the larger circles) are placed in a row, with dimes and quarters alternating (Fig. 4, top).  Now, with every move a dime and an adjacent quarter are moved as one whole, so that they remain adjacent.  You are not allowed to reverse the coins; that is, you should not interchange the dime and the quarter.  Moving the dime and the quarter is considered as one move. The problem is to get the dimes and the quarters in a row in such a way that the dimes are adjacent, and the quarters, too, in as few moves as possible.

Figure 4                                     Figure 5

Be sure to use your MathWorld Interactive six problem-solving steps. Have fun!