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.
2. Ten Coins Problem
The object of this game is to move two adjacent pieces together starting from the beginning formation to the ending formation.
Beginning formation of 5 large and 5 small coins: X O X O X O X O X O (assume X is small coin and O is large coin)
Desired ending formation: O O O O O X X X X X
To move the coins, you take any number of moves. Each move must move two adjacent coins together, either to the left side or the right side of the line of coins. So for the first move, you move either a set of { X O } or a set of { O X }, either to the left or right of the line of coins. The space vacated by the moved coins have no significance, and the resulting line of coins can be shifted and reset over the vacated spaces, but the sequence of coins must remain intact.
For example, the first move might be: X O X {O X} O X O X O Move the { O X } set to the right end of the line, then the
Resulting formation: X O X O X O X O {O X} Where the { O X } has been moved from the center to the right side of the line.
So, in similar fashion, move the coins, always two adjacent coins at time, either { O X }, or { X O }, or { X X } , or { O O }, to the left end or the right end of the line of coins, and achieved the desired ending formation of 5 large coins together, and 5 small coins together.
About six moves should achieve the desired result.
Note: These two games were taught to me by friends, the ten matches game by someone whom I no longer recall, and the ten coins game by a Ms. Cary Chen from Taipei, Taiwan. Perhaps the ten matches game was learnt at a mizu-shobai (water business) bar or club in Tokyo, Japan in the early 1970's.