Looking through the Bulbapedia learnset entries for each HM move, I have found no instances within each HM set where a Pokemon learn it, but its evolution can not;
- Cut (HM01)
- Fly (HM02)*
- Surf (HM03)*
- Strength (HM04)
- Flash (HM05 Gen 1-3)
- Venonat/Venomoth can to learn Flash in Yellow, but not in R/B. Venonat loses the ability to learn flash in Gen 2
- Hoothoot/Noctowl lose the ability to learn Flash in Gen 4, although it's no longer an HM.
- Defog (HM05 D/P/Pt)
- Whirlpool (HM05 Hg/Ss - HM06 Gen 2)
- Waterfall (HM05 Gen 5 - HM07 Gen 2-4)
- Rock Smash (HM06 Gen 3-4)
- Dive (HM06 Gen 5 - HM08 Gen 3)
- Rock Climb (HM08 Gen 4)
There are a few fringe cases that pop up in earlier generations (Mostly between Red Blue and Yellow) where a Pokemon might learn the HM in one game and then be traded to another where its evolution cannot. There may also be unmentioned cases of this between Gens 1 and 2, however the Time Capsule was fairly restrictive in what could be sent back.
*Pikachu is an interesting side case - As there are event and side-game transfers that can give you a Pikachu with Fly, or even Surf (there's also a surfing Pichu). However in none of these instances can Pikachu be taught the moves from an HM.
IV stands for Individual Value.
IVs are a hidden stat that every Pokemon has innately, that cannot be changed after the Pokemon is originally generated. Each Pokemon has six separate IVs, one for each basic stat (Attack, Defense, Special Attack, Special Defense, Speed, and HP). The IV values can range from 0 to 31, with 31 being the best.
The specific equations to calculate stats at a given level include IVs, but it's a pretty complicated ordeal.
Here's the equation for HP:
![enter image description here](https://i.stack.imgur.com/QheI2.png)
And the equation for all the other stats:
![enter image description here](https://i.stack.imgur.com/TFWMV.png)
(Images courtesy of Bulbapedia)
IVs are hidden values, and there is no way to tell them without simply noting your stats and EVs at several different levels and reverse-engineering them using a calculator. A good calculator for this task can be found here.
The best way to test for IVs upon newly hatching or catching a Pokemon is to save the game, then feed it a bunch of Rare Candies while noting its stats each level. After you narrow down its IVs, load the game again. The IVs won't be changed, but you'll have your Rare Candies back to use again.
You can also attempt to breed a Pokemon with the same IV stat as its parent by using a specific EV breeding item. Trust me, trying to get the IVs you want takes forever.
Best Answer
Shown traits
Attack - Increases damage done by physical attacks.
Defense - Amount of damage reduction from physical attacks.
Special Attack - Increases damage done by special attacks.
Special defense - Amount of damage reduction from special attacks.
What determines whether a move is physical or special changed in generation IV. Before Generation IV this was determined by the type of move. For example, both wing attack and gust are flying. Both are also marked as physical because of this. In generations IV and V however, moves are marked physical or special based on the move itself, not its type. This makes more sense now that gust is special and wing attack would be physical.
Speed - The pokemon with the highest speed takes the first turn in a battle
HP - Your pokemon's total hit points, the amount of damage it can take before fainting.
Nature is something you can see and affects all stats depending on which nature a Pokemon has
EV's or Effort Values is a hidden vlaue that also affects Pokemon's stats. There's so much on this topic so it's better to just read the Bulbapedia page for yourself.
IV's or Individual Values are only used by the game to determine the stats of the Pokemon (e.g. when given an egg, found in the wild, or given by an NPC). IV's also determine whether the Pokemon is shiny or not in every generation other than the first.
The only hidden stats are Accurracy and Evasion. Both are explained here with mathematic formulas