Lyf How to reach or beat a GHS? (Part 6)

Counting and Going

Sometimes we should count the moves: “which way is better? “, while sometimes we only go twice to test. It’s hard to way when to take which medicine, perhaps needing experience.
When I was counting, I watched the same processes between the two ways and cut them; then comparing the rest moves.
A typical situation is like this:

Solution #1: push block #1 to water, push block #2 to water.
Solution #2: push block #1 to P2, push block #2 to O2, push block #1 to water, push block #2 to water.
The former cost more moves. Why?
I compare the two processes as below: the “go and return from M2 to N4” unit are the same, cut. “From P1 to P5” are also the same, cut. Sol’n #1 contains a “go and return from M2 to P1”, needing 8 moves, while sol’n #2 only contains a unit.
See Picture 10.1 for a situation:

Picture 10.1

You want to push 5 blocks to P2-P6. How many moves does it cost when you reach P2?
See Picture 10.2.

Picture 10.2

Solution #1: push P15 into water, push O15 to water, push N14 to water, push M13 to water, push L12 to water.
It cost 107 moves (in total). See Picture 10.3.

Picture 10.3

Solution #2: it is like #1. But when you reach this situation—(See Picture 10.4)

Picture 10.4

Go to K12 to push L12 to O12. It will save 2 moves.(Picture 10.5)
It is easily discovered just by “counting”.

Picture 10.5

Is there any way to save more moves? You can see the GHS is 104/171.
See Picture 10.6 for solution #3.

Picture 10.6

Push O15 to P15, push N13 to P13. Go to P14, push a block into the river. Go to P16, push a block into the river. Push M15 to P15, push L13 to P13. Go to P14, push a block into the river, Go to P16, push a block into the river. See Picture 10.7.

Picture 10.7

I personally reached this score only by “going”.
After going and reaching the GHS, I went on to “think”: why Solution #3 is better?
See Picture 10.8: (I edit the map for a needing situation)

Picture 10.8

I divide the Solution #3 into 2 phases. See first phase: only O15 and N13 are involved. In order to push them into water I need at least 14 extra moves. 14 moves= 2 units + 2 moves, that means if I change the position of N13, from N13 to N14, we also need 14 EXTRA moves. And yes, that means, if I put the 2 blocks on N7 and O8, like Picture 10.9:

Picture 10.9

We still need 14 EXTRA moves.
Then we put the other 2 blocks on the map. See Picture 10.10.

Picture 10.10

It will cost the same moves as Solution #3.
We compare this situation with Solution #2. We can find the essential difference is the two blocks farther away from us. Therefore, if we change Picture 10.2 into Picture 10.11:

Picture 10.11

We can reach the same score as Solution #3.
Now we only watch the far-away 2 blocks: (Picture 10.12)

Picture 10.12

Why it is better than Picture 10.13, while Picture 10.8 costs the same moves as Picture 10.9?(The following is Picture 10.13—I suppose L12 must be pushed right to P12 instead up to L11)

Picture 10.13

In picture 10.12, the vertical extra move is 6 moves and the horizontal extra move is 12(total 18). In Picture 10.13, the vertical extra move is 6 moves and the horizontal extra move is 14(total 20). In Picture 10.8, the vertical extra move is 6 and the horizontal extra move is 8(total 14). In Picture 10.9, the vertical extra move is 4 moves and the horizontal extra move is 10(total 14). Watch, 4 moves! Why in Picture 10.13 the vertical extra move cannot be 4?
Because the difference between 4 and 6 in Picture 10.13, it is just like the difference between solution #1 and #2! In Solution #1, the vertical extra move is 4, but the horizontal extra move is too many because the other block is too far away. Since the vertical move cannot be 4, Picture 10.12 is better than 10.13.
After some thinking you can go deep into the logic and make faster progress. For example, after writing the above analysis I suddenly found that I can beat GHS!
See Picture 10.14:

Picture 10.14

Push O15 into water, then push L10/N12/O14 to P10/P12/P14, then push them into water.
How did I think out this Solution #4?
Because through the above analysis I got to know that I can freely send the single block at Column O into water at any time because it has no influence with the block at Column N. So, how about changing “two by two” into “1+3”? Luckily the latter way costs less moves.
Then, how about “0+4”? See Picture 10.15.

Picture 10.15

It cost the same moves as Picture 10.14.
See Picture 10.15 as an important situation and 10.16 as the ending:

Picture 10.16

Picture 10.17

The new GHS doesn’t mean that the earlier analysis is useless. On the contrary, without the analysis I couldn’t think out these new solutions in this particular level.
So, try to go and think.

This tutorial is written by Li YiFeng nick lyf.