"tapperino_forums;c-1623572" wrote:
"meinaz;c-1623448" wrote:
Look at the order @davejandals posted above. It is the most efficient way to find the gem. You want to space out the holes so each square is only checked by one hole instead of multiple. (Hopefully that makes sense.)
Thanks, yes. I drew out happygamer73's version, as it is slightly more efficient. And if you alter the sequence it's easier to remember and do - as in effect it is chess moves of a knight all the way up to include 8, and then 9 and 10 in the last two corners.
http://i.imgur.com/aJqrQa7.jpg
http://i.imgur.com/KricXmi.jpg
So, while it may have the same maximum number of moves, do you think that it might be less efficient on average because you are not checking as many spots early on?
In the top version, you have checked for the possibility of the gem in 15 squares by the 3rd move. While in the bottom version you have only checked 13 squares.
Most of the time you won't need all 10 shovels to get to the gem. So not only do we want the least possible moves, but also the lowest average moves. In fact, I would argue that the lowest average is more important than the lowest maximum.
I haven't done the math yet on long term averages. This is just a gut feeling about what that math might reveal.
