Does anyone know how many difficulty levels the battle Maison goes to?
There are 20 for the regular categories, but for the Super categories there isn't a limit. However, after 50 Super battles you fight the Battle Chatelaine, and if you beat her you get a statue to commemorate it. So I guess 50 is the number to aim for.
I'm having a hard time locating a good Hidden Power guide for Gen 6...
Ultimately I want to be able to know any and every possible IV combination that can result in a Hidden Power Ice.
Edit: I have a lot of 31s in the breeding groups to work with. If I can know what IVs are acceptable, it should be an easy matter of checking the exact IVs of some pokes, and knowing which imperfects stats could be beneficial.
Okay, let's give this a go. There's an explanation of the process here:
https://www.serebii.net/games/hidden-power.shtml
You can see in the above link that if the formula outputs 13, then the Hidden Power type is Ice.
So we have to find all solutions of the equation
Floor(15 * (HP + 2Att + 4Def + 8Spe + 16SpA + 32SpD)/ 63) = 13
where HP takes values of 1 if the HP IV is odd and 0 if it is even, Att takes values of 1 if the Attack IV is odd and 0 if it is even, and so on.
The floor function takes the integer part of a number, so we can also write this as
13 < 15 * (HP + 2Att + 4Def + 8Spe + 16SpA + 32SpD)/ 63 < 14
Multiply by 63/3 = 21:
273 < 5HP + 10Att + 20Def + 40Spe + 80SpA + 160SpD < 294
Note that 5HP + 10Att + 20Def + 40Spe + 80SpA + 160SpD is a multiple of 5, so all solutions are of the form
5HP + 10Att + 20Def + 40Spe + 80SpA + 160SpD = 275 or 280 or 285 or 290
Or, dividing by 5:
HP + 2Att + 4Def + 8Spe + 16SpA + 32SpD = 55 or 56 or 57 or 58
Note that, because the required total is so high, the variable SpD MUST be 1. Therefore the Pokemon must have odd Special Defense IVs. So we can remove that part of the equation by subtracting 32:
HP + 2Att + 4Def + 8Spe + 16SpA = 23 or 24 or 25 or 26
Again, we can see that it is impossible to achieve such a high total unless SpA = 1. Therefore the Pokemon must have odd Special Attack IVs, and we remove that part of the equation:
HP + 2Att + 4Def + 8Spe = 7 or 8 or 9 or 10
Now we can see that it IS possible to have Spe = 0, but only if HP = Att = Def = 1. And if Spe = 1, then the possibilities are HP = 1, Att = 0, Def = 0 or HP = 0, Att = 1, Def = 0 or HP = 0, Att = 0, Def = 0.
We have therefore calculated all possibilities! Hooray! Let's summarise:
In order to achieve an Ice-type Hidden Power, the Pokemon's IVs must satisfy the following:
Either
HP odd
Attack odd
Defense odd
Special Attack odd
Special Defense odd
Speed even
Or
HP odd
Attack even
Defense even
Special Attack odd
Special Defense odd
Speed odd
Or
HP even
Attack odd
Defense even
Special Attack odd
Special Defense odd
Speed odd
Or
HP even
Attack even
Defense even
Special Attack odd
Special Defense odd
Speed odd
Of course, assuming you want the IVs in each stat to be as high as possible, just replace "odd" with "31" and "even" with "30".
I should make a thread with these calculations for all of the types.