6th Gen X/Y Hidden Power Guide

[Banned]

~X/Y Hidden Power Guide~

We've always had Hidden Power calculators such as https://www.psypokes.com/dex/hp.php to work out a particular Pokemon's Hidden Power type and power given its IVs. But what about the other way round? It's often the case that we want to find out which IVs we should breed into our Pokemon to give the type and power we want for Hidden Power. Sure, we have the table in the above link, but that table is outdated and doesn't give us the whole story.

In previous generations this reverse engineering was difficult to say the least, but with the advent of X and Y the Hidden Power mechanics were made a whole lot simpler with the removal of power as a variable, instead giving it a fixed power of 60. This has made calculating the required IVs for the desired Hidden Power much more manageable. So let me deal with the mathematics of it all, and you can enjoy the results: this guide!

First of all, let me give you an example of the calculations involved so that you can convince yourselves that what I'm doing is valid mathematics and not just "magic" (all calculations are based on https://www.serebii.net/games/hidden-power.shtml).

Example:

Spoiler:

In this example we will go through the calculations for an Ice-type Hidden Power.
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".

Now, the required IVs for each type are as follows:

FIGHTING

Spoiler:

Either
HP even
Attack even
Defense even
Special Attack even
Special Defense even
Speed even

Or
HP odd
Attack even
Defense even
Special Attack even
Special Defense even
Speed even

Or
HP even
Attack odd
Defense even
Special Attack even
Special Defense even
Speed even

Or
HP odd
Attack odd
Defense even
Special Attack even
Special Defense even
Speed even

Or
HP even
Attack even
Defense odd
Special Attack even
Special Defense even
Speed even

FLYING

Spoiler:

Either
HP odd
Attack even
Defense odd
Special Attack even
Special Defense even
Speed even

Or
HP even
Attack odd
Defense odd
Special Attack even
Special Defense even
Speed even

Or
HP odd
Attack odd
Defense odd
Special Attack even
Special Defense even
Speed even

Or
HP even
Attack even
Defense even
Special Attack even
Special Defense even
Speed odd

POISON

Spoiler:

Either
HP odd
Attack even
Defense even
Special Attack even
Special Defense even
Speed odd

Or
HP even
Attack odd
Defense even
Special Attack even
Special Defense even
Speed odd

Or
HP odd
Attack odd
Defense even
Special Attack even
Special Defense even
Speed odd

Or
HP even
Attack even
Defense odd
Special Attack even
Special Defense even
Speed odd

GROUND

Spoiler:

Either
HP odd
Attack even
Defense odd
Special Attack even
Special Defense even
Speed odd

Or
HP even
Attack odd
Defense odd
Special Attack even
Special Defense even
Speed odd

Or
HP odd
Attack odd
Defense odd
Special Attack even
Special Defense even
Speed odd

Or
HP even
Attack even
Defense even
Special Attack odd
Special Defense even
Speed even

ROCK

Spoiler:

Either
HP odd
Attack even
Defense even
Special Attack odd
Special Defense even
Speed even

Or
HP even
Attack odd
Defense even
Special Attack odd
Special Defense even
Speed even

Or
HP odd
Attack odd
Defense even
Special Attack odd
Special Defense even
Speed even

Or
HP even
Attack even
Defense odd
Special Attack odd
Special Defense even
Speed even

BUG

Spoiler:

Either
HP odd
Attack even
Defense odd
Special Attack odd
Special Defense even
Speed even

Or
HP even
Attack odd
Defense odd
Special Attack odd
Special Defense even
Speed even

Or
HP odd
Attack odd
Defense odd
Special Attack odd
Special Defense even
Speed even

Or
HP even
Attack even
Defense even
Special Attack odd
Special Defense even
Speed odd

Or
HP odd
Attack even
Defense even
Special Attack odd
Special Defense even
Speed odd

GHOST

Spoiler:

Either
HP even
Attack odd
Defense even
Special Attack odd
Special Defense even
Speed odd

Or
HP odd
Attack odd
Defense even
Special Attack odd
Special Defense even
Speed odd

Or
HP even
Attack even
Defense odd
Special Attack odd
Special Defense even
Speed odd

Or
HP odd
Attack even
Defense odd
Special Attack odd
Special Defense even
Speed odd

STEEL

Spoiler:

Either
HP even
Attack odd
Defense odd
Special Attack odd
Special Defense even
Speed odd

Or
HP odd
Attack odd
Defense odd
Special Attack odd
Special Defense even
Speed odd

Or
HP even
Attack even
Defense even
Special Attack even
Special Defense odd
Speed even

Or
HP odd
Attack even
Defense even
Special Attack even
Special Defense odd
Speed even

FIRE

Spoiler:

Either
HP even
Attack odd
Defense even
Special Attack even
Special Defense odd
Speed even

Or
HP odd
Attack odd
Defense even
Special Attack even
Special Defense odd
Speed even

Or
HP even
Attack even
Defense odd
Special Attack even
Special Defense odd
Speed even

Or
HP odd
Attack even
Defense odd
Special Attack even
Special Defense odd
Speed even

WATER

Spoiler:

Either
HP even
Attack odd
Defense odd
Special Attack even
Special Defense odd
Speed even

Or
HP odd
Attack odd
Defense odd
Special Attack even
Special Defense odd
Speed even

Or
HP even
Attack even
Defense even
Special Attack even
Special Defense odd
Speed odd

Or
HP odd
Attack even
Defense even
Special Attack even
Special Defense odd
Speed odd

GRASS

Spoiler:

Either
HP even
Attack odd
Defense even
Special Attack even
Special Defense odd
Speed odd

Or
HP odd
Attack odd
Defense even
Special Attack even
Special Defense odd
Speed odd

Or
HP even
Attack even
Defense odd
Special Attack even
Special Defense odd
Speedodd

Or
HP odd
Attack even
Defense odd
Special Attack even
Special Defense odd
Speed odd

Or
HP even
Attack odd
Defense odd
Special Attack even
Special Defense odd
Speed odd

ELECTRIC

Spoiler:

Either
HP odd
Attack odd
Defense odd
Special Attack even
Special Defense odd
Speed odd

Or
HP even
Attack even
Defense even
Special Attack odd
Special Defense odd
Speed even

Or
HP odd
Attack even
Defense even
Special Attack odd
Special Defense odd
Speed even

Or
HP even
Attack odd
Defense even
Special Attack odd
Special Defense odd
Speed even

PSYCHIC

Spoiler:

Either
HP odd
Attack odd
Defense even
Special Attack odd
Special Defense odd
Speed even

Or
HP even
Attack even
Defense odd
Special Attack odd
Special Defense odd
Speed even

Or
HP odd
Attack even
Defense odd
Special Attack odd
Special Defense odd
Speed even

Or
HP even
Attack odd
Defense odd
Special Attack odd
Special Defense odd
Speed even

ICE

Spoiler:

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

DRAGON

Spoiler:

Either
HP odd
Attack odd
Defense even
Special Attack odd
Special Defense odd
Speed odd

Or
HP even
Attack even
Defense odd
Special Attack odd
Special Defense odd
Speed odd

Or
HP odd
Attack even
Defense odd
Special Attack odd
Special Defense odd
Speed odd

Or
HP even
Attack odd
Defense odd
Special Attack odd
Special Defense odd
Speed odd

DARK

Spoiler:

HP odd
Attack odd
Defense odd
Special Attack odd
Special Defense odd
Speed odd

~~~

Note: There is currently no Fairy-type Hidden Power.

Note: Assuming you want the IVs in each stat to be as high as possible, just replace "odd" with "31" and "even" with "30".

Comment below if you have any questions or feedback.