The object of this game is to move matches one at a time from a beginning formation to the ending formation, like this:
Beginning formation of 10 matches: I I I I I I I I I I
Desired ending formation: X X X X X
Each X is formed by two matches, and a move consists of moving one match at a time. To move a match, you may move the match in either direction, left or right, by jumping the match over exactly two matches. Of course, the matches at the end of the string of matches can over jump into the main body of the string of matches. The match at either end may not be curled around to the other end of the string of matches.
A move must consist of selecting any match you wish, and jumping over exactly two matches, going either left or right, and forming an X with the match that the jumping match lands on. A few examples of moves are given below.
1. For ease, number the matches 1 - 10.
I I I I I I I I I I
. match no. 1 2 3 4 5 6 7 8 9 10
2. You select no. 9 and jump over no. 7 and 8 I
I I I I X I I I
. match no. 1 2 3 4 5 6/9 7 8 10
3. You then select no. 7 and jump over no 6.
I I I I X X I I
. (which has two matches, 6 and former no. 9) 1 2 3 4 5/7 6 8 10
4. You then jump no. 1 over no. 2 and 3.
I I X X X I I
. 2 3 4/1 5 6 8 10
5. When you reach this point, unfortunately, further moves are no longer possible, because a move must consist of a single match jumping over exactly two matches, whether the two matches are standing by themselves or already formed as an X. In the formation reached in step 4 above, such a move is no longer possible. Therefore, you must consider carefully the beginning moves so as to always leave the possibility of further moves involving jumping over two matches.
Good luck in this match game. Several variations are possible to achieve
your end result.