KnightFighter: er...if it moved 2 spaces at a time it wouldn't be possible to hit all the spaces on the board...that looks like an initial problem...

nodnarbo: please note, there will be two players, and you can move in any direction including empty spaces ... I think it's possible to cover all the squares unless blocked by the opponent. In case moves are blocked, the player with more points wins the game ... I do not see this as a problem, since this is not a solitaire game with the objective to touch every square ... thanks for your comment.
Andy.

KnightFighter: one more thing: remember, that many squares will be cleared by the rules of mirrors and doubles ... so there will not be a need to touch every square and not even required.
Andy.

KnightFighter: does it have to move 2 spaces each turn, or can it choose 1 or 2?

nodnarbo: no choice, 2 squares at the time.
It's faster and powerfully strategic. Each and every move not only removes points from the squares Plow goes thru but also cancells mirrors and any chosen double .somewhere on the board. So 4 tiles are stripped from the points after each move... now, the whole idea is to choose the proper direction and not only to collect points from the squares you go thru, but to eliminate points from the opponent's path ...
Andy.

KnightFighter: so with your current rules, each player will be able to land on or move through exactly 40 of the 64 spaces on the board. (if you don't understand why, get out a board and try it.) so depending on the placement of each players pieces, it might be possible for 24 spaces to be 'untouchable'.

What if each player had 2 pieces that start in opposite corners. so one player's pieces would start in the upper left and lower right corners, and the other player's pieces in the upper right and lower left.

nodnarbo: I am talking about 100 squares board like for Knight Fight ... I think you are trying to play solitaire-like game and go around the board and make some kind of record ... this is not the idea I have in mind ... don't worry how many squares you cover during the game, think about collecting points while you move and if the game stops (for whatever legal reason) ... it stops, compare your points and that's it. They have one piece each, not two ... it's enough problems to solve with one piece on each side.
Andy.

KnightFighter: oh, 10x10, not 8x8, my bad, now there are 35 spaces that can't be touched, so...the players can choose where their pieces start?

nodnarbo:

maybe we solve the problem like this:
the pieces always have to move 2 steps. but an empty square does not count!

diogenysos: you wanted to say that plow HAS to remove two numbers ? right ? no matter how long is the path ? I think it's s a trap ... look at the diagonal, for example ... there are two numbered squares at the other end that plow resides ... so the plow has to go along the whole diagonal to get the numbered squares, simply because, empty squares do not count ? No, it wasn't my idea. Plow moves 2 squares no matter what ... thanks for your comments ...
Andy.

KnightFighter: oh, i was not considering diagonal moves, stupid me.

I can see this game working on a board with an odd number of spaces on each side, but with an even number of spaces on each side it leaves 2 edges unavailable to each player...

nodnarbo: you are not stupid, do not say this about yourself... we are learning and trying to invent something ... I honestly do not know how you got this idea about two edges ... but, do we really need to care about this ... look, as a first player you put you plow on any numbered square and collect points from this square ... your opponent does the same. After these two moves any mirrors are removed or, if you stepped on a double you chosen any double to be removed. In your next move you move two places in any chosen direction and collect points for this move. At the same time any two mirrors are removed from the board ... game continue this way until there is no more numbered squares on the board ... when the board is becoming emptier, plows are racing two spaces to get to numbered squares ... in my opinion all the numbered squares can be cleared unless there is a situation I cannot see right now ... but even then it's easy to determine the winner ...
Andy.

KnightFighter: hm...I'll put it this way, you start with your plow in the bottom left corner, say, we'll call this space a1. you move 2 spaces to the right and you are now on c1, continue moving this way and you will eventually get to i1, but j1 is unreachable, because you can only move one space in that direction.

nodnarbo: ok, I got it ... do you think it would be better to collect two squares in the first move ? it would solve this problem, since starting at a1 and moving to b1 (as a one move) will open the door to j1 ...
Andy.