Alright, so I ran a few tests trying to isolate as many variables as possible so we can start trying to deduce some stuff. I picked up a 6IV Ditto and a few pokemon I had lying around, a Destiny Knot, an Everstone, and started breeding things. I'll dump my results below and my analysis on it, and would greatly appreciate if others could attempt to replicate the results under similar conditions so as to validate our conclusions, or even draw new ones.

First of all, my goal was to determine whether it is possible to influence a child's IVs by swapping parents between Soft Resets, while trying to isolate as many variables as I can. First of all, notation:

0 -> No Good
1 -> Decent
2 -> Pretty Good
3 -> Very Good
4 -> Fantastic
5 -> Best

So I took a Chinese 6IV Ditto and 2 English 4IV Rowlets, each with a different IV spread. The experiment consisted of depositing Ditto holding an EVERSTONE in the Daycare, and then saving. From there, deposit the first Rowlet with a DESTINY KNOT, make and hatch 5 eggs, note down IVs. Soft reset, deposit the second Rowlet with the destiny knot, make and hatch 5 eggs, note down IVs.

For simplicity, we will label Ditto as Parent A and the Rowlets as Parent B. Thus, I present to you guys the result I stumbled upon:

Parent A: 5/5/5/5/5/5 @ Everstone
Parent B: 5/5/5/2/5/2 @ Destiny Knot

Child 1: 5/1/5/5/5/5 -> Random roll was Atk (1)
Child 2: 5/5/5/2/2/5 -> Random roll was SpDef (2)
Child 3: 5/5/5/5/5/1 -> Random roll was Spd (1)
Child 4: 5/5/5/3/5/5 -> Random roll was SpAtk (3)
Child 5: 3/5/5/5/5/2 -> Random roll was HP (3)

Parent A: 5/5/5/5/5/5 @ Everstone
Parent B: 3/2/5/5/5/5 @ Destiny Knot

Child 1: 5/1/5/5/5/5 -> Random roll was Atk (1)
Child 2: 5/2/5/5/2/5 -> Random roll was SpDef (2)
Child 3: 5/5/5/5/5/1 -> Random roll was Spd (1)
Child 4: 5/5/5/3/5/5 -> Random roll was SpAtk (3)
Child 5: 3/5/5/5/5/5 -> Random roll was HP (3)

Note how the random stat chosen by destiny knot is always the same, and how it has ALWAYS the same value. We can't really draw much conclusion from this other than that, and so we need further experimenting. Now, I got a 0 IV Rowlet to hatch 5 more eggs with. With this, we can see if the inherited stats are matching which parent is giving them away. Here are the results:

Parent A: 5/5/5/5/5/5 @ Everstone
Parent B: 1/1/1/1/2/2 @ Destiny Knot

Child 1: 5/1/1/5/5/5 -> Random roll could be Atk (1)
Child 2: 5/1/1/1/2/5 -> Random roll could be SpDef (2)
Child 3: 5/5/5/5/5/1 -> Random roll was Spd (1)
Child 4: 5/5/1/3/5/5 -> Random roll was SpAtk (3)
Child 5: 3/5/5/5/5/2 -> Random roll was HP (3)

We can note that, for child 1, the HP stat is always inherited from Parent A. The same goes for SpAtk, SpDef and Spd. Def is always inherited from Parent B, but there's no real way to be sure. Atk is ALWAYS the same, suggesting it's a common random roll.

For child 2, HP and Spd come from A, while everything else except SpDef, from B, following a similar analysis.

For child 3, everything comes from Parent A, except the random roll, Spd.

Similar coincidences happen with children 4 and 5, too. We can then conclude that we can swap the parent before making the eggs to successfully manipulate the child's IVs. With this, it's possible to time machine your way into a perfect child with a 1/32 odds for any species, assuming you have appropriate parents for the job. Even though it wasn't tested, it's safe to assume Gender, Shininess, Nature and Ability would be equal between sets of children, so long as the requirements are the same (50/50 gender species only, cannot swap regular ability for HA, etc). That's fine and all, but is it safe to assume this stays the same if we change species?

I now took a 0IV English Dragonite and repeated the same process, with soft reset, destiny knot and hatching 5 eggs. The results:

Parent A: 5/5/5/5/5/5 @ Everstone
Parent B: 3/1/2/0/3/2 @ Destiny Knot

Child 1: 3/1/5/0/3/2 -> Random roll could be Atk (1)
Child 2: 3/5/5/5/2/2 -> Random roll was SpDef (2)
Child 3: 3/1/2/0/3/1 -> Random roll was Spd (1)
Child 4: 3/1/5/3/3/2 -> Random roll was SpAtk (3)
Child 5: 3/1/2/0/3/5 -> Random roll could be HP (3)

Well, bummer. It seems things are off by quite a lot, but let's give it a try anyway. Assuming that, for child 1, the random roll was Atk, we have that:

HP, SpAtk, SpDef and Spd were inherited by B
Def was inherited by A

Oddly enough, that is the SAME result as the previous ones with Rowlets... Except Parents A and B are reversed. It's as if A and B became B and A when the Destiny Knot chose whose stats are passed down. To be sure, let's do children 2 and 3:

Child 2: SpDef random, HP and Spd from B, rest from A
Child 3: Spd random, everything else from B
Child 4: SpAtk random, Def from A, everything else from B

So it does match after all! Except it inverts things for some odd fucking reason. Weird. The only thing that changed was the species, and well, the egg group. So let's pick something from another egg group, like Luvdisc. And why not also pick something from a different region, too.

This time, I got a Japanese 0IV Luvdisc and repeated the process. The results:

Parent A: 5/5/5/5/5/5 @ Everstone
Parent B: 2/1/3/1/2/1 @ Destiny Knot

Child 1: 2/1/5/1/2/1 -> Random roll could be Atk (1)
Child 2: 2/5/5/5/2/1 -> Random roll could be SpDef (2)
Child 3: 2/1/3/1/2/1 -> Random roll could be Spd (1)
Child 4: 2/1/5/3/2/1 -> Random roll was SpAtk (3)
Child 5: 3/1/3/1/2/5 -> Random roll was HP (3)

Now, let's analyze the results and compare...

Child 1: Atk could be random, Def from A, rest from B
Child 2: SpDef could be random, HP and Spd from B, rest from A
Child 3: Spd could be random, everything else from B
Child 4: Spatk random, Def from A, everything else from B

What do you know, a perfect match with the previous experiment. So changing egg groups is affecting the destiny knot result somehow, but which IVs are inherited are FIXED, as well as their combinations. The only varying factor is who acts as Parent A and who acts as Parent B.

I would perform more experiments, but it is late. Some things to be tested:

> Not using a Ditto at all
> Different species, same egg group
> Does this affect gender/nature/ability at all
> What happens if I swap out the Everstone instead of Destiny Knot
> What if there is no Destiny Knot, does the pattern repeat

So there you have it, lovelies. Get to work, science needs you.