This problem is about a combination lock which consists of 5 wheels with 4 possible symbols each, which turn one step in any direction ( like the bike combination locks), but what is special about this one is the fact that each wheel can't be rotated individually. Every time a wheel is turned, 2 more also turn always one step at a time. The following operations are the only ones possible:
We will call a clockwise wheel turn: +1 and a couterclockwise wheel turn: -1
1.. +1 -1 +1 0 0
2.. +1 +1 0 0 -1
3.. 0 -1 +1 -1 0
4.. -1 0 0 +1 +1
5.. 0 0 -1 +1 +1
My question is: How can one, given an initial combination of symbols calculate what sequence of the above operations is needed to get to a final combination of symbols?
Example: If the 4 symbols of each wheel are named A,B,C,D,E and let's say the initial combination is C,E,D,A,B how can we get to E,C,A,D,B ? or from any initial to any final combination. What is the math or formulas which allow for this calculations?. Thanks beforehand guys.
We will call a clockwise wheel turn: +1 and a couterclockwise wheel turn: -1
1.. +1 -1 +1 0 0
2.. +1 +1 0 0 -1
3.. 0 -1 +1 -1 0
4.. -1 0 0 +1 +1
5.. 0 0 -1 +1 +1
My question is: How can one, given an initial combination of symbols calculate what sequence of the above operations is needed to get to a final combination of symbols?
Example: If the 4 symbols of each wheel are named A,B,C,D,E and let's say the initial combination is C,E,D,A,B how can we get to E,C,A,D,B ? or from any initial to any final combination. What is the math or formulas which allow for this calculations?. Thanks beforehand guys.