I have a problem that I have been working on for which I cannot find a solution.
Problem: Assume you are on a cartesian plane, and you want to move a die to a specific point. You can move the die up, down, left, right to get to the target. You want to move the die in such a manner that you are minimizing the sum of the visible face.
I have given this some thought and the solution I came up with was that you always move to the largest side that is still going in the direction on the target.
so for example if you were on a 10X10 graph, the die started at (-5,5) and the die was situated as such:
2
___
4| 1 |3
___
5
And you wanted to get to the point (5,-5) then you would move down 5 and the die would look like this:
6
___
4| 2 |3
___
1
My idea behind this is that in moving in the direction of the largest valued side that goes in the direction of the target, you would expose the smallest possible value to be the exposing face, therefore minimizing the sum.
Now I am not sure if this method really works, I cannot seem to find a solution anywhere. I wanted to check and see if this would actually work but I am not sure how to.