Lyf How to reach or beat a GHS? (Part 3)

Even & odd

Imagine a 16*16 field, whose cells are painted black and white one by one, like the chessboard. So, when our tank makes one move, the color under it changes. That is, if we put a flag on a grid which has the same color as your tank’s original position, your moves to the flag must be an even number. On the other hand, If Flag and your tank stand at grids with different colors, you will get a odd number.
If we only consider old-school levels (not including ice/thin ice/tunnels), your score and the GHS must have the same parity, with only 2 exceptions: 1. There are more than 1 flag; 2. There are tank-movers; but if you are sure that the way to use tank-movers should not be changed, the parity will keep the same.
Eg. #0635—the previous GHS is 234/259 and tank-movers should be used in only one way: go up to Line 1 and down to shoot blocks for 5 times. So VVI must got I1, not H1. I tried H1 and luckily beat the GHS by 1 move. If I wanted to reach I1, I have to be 2/4/6… moves better than GHS (here we don’t consider about the shots). It’s hard to say which strategy is better though I1 is nearer to our tank and the map is symmetrical.

Picture 6.1 & 6.2 show the beginning and ending:

Picture 6.1

Picture 6.2

Eg. #0368—Although there are many tank-movers, yet in my strategy, I only use L6&P6-P9 once. My way to use tank-movers cannot be changed but Ihab’s GHS is 174 moves while mine is an odd number. Plus there is a fairly big distance between his and my shots, I believe that I found a shortcut strategy so got much confidence even though my moves was 300+ yet. After efforts the GHS was beaten.
In some cases the parity of shots can show its importance. Eg. #0334—I managed to reach the flag with a score of 58/63. But I cannot make any progress with my strategy. How to reach =H.L’s 56 moves? The key is the parity of shots. His shots is 62, different parity from mine. But in my strategy, to minimum the score, 4 blocks must go to O1, E1, F1 and I5. G12 must go to I10 and I9 should keep alive. There is nowhere to change the parity of shots. Therefore, I had to find another strategy. With the confidence I found it, leaving the mirror at G11.

Picture 7.1 shows the beginning:

Picture 7.1

Picture 7.2 shows the ending of the 1st strategy:

Picture 7.2

Picture 7.3 shows the ending of 2nd strategy:

Picture 7.3

Thanks for reading this article.

This tutorial is written by Li YiFeng nick lyf.