On the 5th-6th week, AI opponents arrive with 10 spell power and Chain Lightning; their attack must be survived with minimal losses. Again, the red and blue castles must be captured as early as possible. Also, the AI's Inferno must be killed by the 4th-5th month—otherwise, they might assemble a simply unstoppable fist. On normal maps, it would be easy, but when all magic schools are banned and spells are available only at levels 1-2 and without Blind, losses are inevitable. Log is not banned on the map, so the only bonus is in gloves against 8 atk.
Added after 2 hours 38 minutes
So, details on the "last" step, information taken from
http://heroescommunity.com/viewthread.php3?TID=27539, rewritten here in my own words + supplemented with screenshots as proof:
The general rule here is as follows:
if your number of move points is between 100*k and 141*k, then a diagonal step costs the same as a horizontal/vertical one. This depends on nothing except k—the terrain movement penalty:
swamp 175%, sand and snow - 150%, rocks - 125%, all other terrain types - 100%
it is also reduced by pathfinding by 25% for each upgrade level, but k cannot be lower than 100%
a special case occurs if there is a nomad in the army and the terrain is sand. In this case, k=100% regardless of the pathfinding upgrade level.
Now the consequences:
1) The last step exists on all terrain types For terrains without penalties, if 100<=move points<=141, then any hero with any army can make a diagonal step.
For terrains with a penalty and an insufficiently upgraded pathfinding level (regardless of the army), you can always make a diagonal step instead of a horizontal/vertical one. Also, note that after a diagonal step, there may be remaining move points sufficient for a step on a road.


2) If you have native troops but under-leveled pathfindinga) For rocks, you need to have 125<=move points<=176 to be able to make a diagonal step. But at 141 move points, you would have enough for movement without a penalty anyway, and the maximum remainder would be 176-141=30, which is insufficient even for a step on fast roads, so it would reset to zero and you wouldn't notice the discount. Only at 125<=move points<=140 would you feel the last step—this is a small range, which explains why it's so rarely seen in practice.
b) For snow, the discount range is 150<=move points<=212, and there are two points here:
- at 200<=move points<=212, we get a discount on the diagonal step and spend 100 move points, but 100 to 112 move points still remain, and we can make another horizontal/vertical step. Thus, we observe the phenomenon of the "penultimate" step :) The range for observing this phenomenon is small, but it includes the value of 200 move points, so it may be observed quite often.

- at 150<=move points<200, during a diagonal step, we get a discount and are left with 50 to 99 move points, which we can spend on a step only if we have reached a road.
c) For sand with native units moving without a penalty—none.
As for the nomad—the mechanic with him is exactly the same as if you had advanced pathfinding upgraded only for sand.
d) For swamp, the discount range is 175<=move points<=247, but with the exception of the values, the snow features are repeated here—there is no last step, but there is a penultimate step. And it is exactly in the swamp that the penultimate step is discovered more easily and most often.
3) Diagonal step discount and roadsI repeat, for the discount calculation, it doesn't matter what the move points are spent on. The main thing is that their current value is within a certain interval. For terrain without penalties, this is 141-100=41 move points. For rocks 51, snow and sand - 62, for swamp 72. As is known, for fast roads a step costs 50 move points, for medium 65, and they do not require pathfinding!, which means that in some cases we can get a discount on a diagonal step for as many as two moves.
For example, you have 200 move points on a fast road on snow. Then
1) If you don't have pathfinding, you can make the first diagonal step on the road with a discount of -50mp,
you have 150 mp left—this also falls within the discount range and you can make a second diagonal step with a discount, and the remaining 100 mp will be spent on two horizontal steps. Total of 4 steps in such a road configuration

2) But if in this situation we place a hero with basic pathfinding, then our hero will only make 3 steps:
1st diagonal step at 200 mp—does not fall within the 125-176 range, so the step cost is 70 mp
2nd diagonal step at 130 mp—falls within the discount range, 130-50=80 mp remain
3rd step: there are only enough move points for one last horizontal step.
Thus, there are situations where pathfinding can ruin your logistics on roads!

And for reference, the maximum move points we can save is 26+72=98. If in a swamp on medium roads, for example with 247 move points, we first make a diagonal step on the road, and then with a penalty—a diagonal step off-road.