Can you breed to get perfect stats?

Question

Say you want to have a pokemon with all the best possible IV's. Would the following work?

1. Find pokemon with perfect IV's in each stat (each pokemon will be referred to by its perfect IV).
2. Breed them all into the same egg group
3. Breed HP with Attack, holding appropriate power items.
4. Breed this new pokemon HP+Attack (holding power weight) with the perfect defensive IV holding a power belt.
5. Breed this new pokemon HP+Defense (holding power belt) with HP+Attack (holding power bracer)
6. Breed HP+Attack+Defense (holding power weight) with Sp. Atk (holding power lens)
7. Breed this new pokemon, HP+Sp. Atk (holding power lens) with HP+Attack+Defense (holding power bracer).
8. Breed this new pokemon, HP+Sp. Atk+Attack (holding power lens) with HP+Attack+Defense (holding power belt).
9. Breed this new pokemon, HP+Sp. Atk+Attack+Defense (holding power weight) with Sp. Def, holding power band.
10. Breed this new pokemon, HP+Sp. Def (holding power band) with HP+Sp. Atk+Attack+Defense (holding power bracer).
11. Breed this new pokemon, HP+Sp. Def+Attack (holding power band) with HP+Sp. Atk+Attack+Defense (holding power belt).
12. Breed this new pokemon, HP+Sp. Def+Attack+Defense (holding power band) with HP+Sp. Atk+Attack+Defense (holding power lens).
13. Breed this new pokemon, HP+Attack+Defense+Sp. Attack+Sp. Def (holding power Weight) with Speed (holding power anklet).
14. Breed this new pokemon, HP+Speed (holding power Anklet) with HP+Attack+Defense+Sp. Attack+Sp. Def (holding power Bracer).
15. Breed this new pokemon, HP+Speed+Attack (holding power Anklet) with HP+Attack+Defense+Sp. Attack+Sp. Def (holding power Belt).
16. Breed this new pokemon, HP+Speed+Attack+Defense (holding power Anklet) with HP+Attack+Defense+Sp. Attack+Sp. Def (holding power Lens).
17. Breed this new pokemon, HP+Speed+Attack+Defense+Sp. Atk (holding power Anklet) with HP+Attack+Defense+Sp. Attack+Sp. Def (holding power band).
18. You now have HP+Attack+Defense+Sp. Atk+Sp. Def+Speed

Answer 1

No, this would never work. When you breed two Pokemon, the baby Pokemon can only inherit at most 3 IV stats (from any parent). The other 3 stats are always random.

The power items allow you to pass one specific stat down to the child. This is the only way to guarantee a particular stat. Only one stat from a power item is guaranteed, so if each parent holds a different power item, the chance is 50/50 for each (plus there is a chance the other stat could be selected as part of normal inheritance).

Here's the key thing: if you have 2 Pokemon with max IVs across the board, breeding them will not make another with all max IVs. The egg is only guaranteed to have 3 perfect IVs. The rest are random so they could even be anything - even zero!