TMs/ HMs:
Here is the list of TMs and HMs that you can have (Note: They are not numbered because of multiple moves being the same number through different gens):
TMs:
Mega Punch
Razor Wind
Swords Dance
Whirlwind
Mega Kick
Toxic
Horn Drill
Body Slam
Take Down
Double-Edge
BubbleBeam
Water Gun
Ice Beam
Blizzard
Hyper Beam
Pay Day
Submission
Counter
Seismic Toss
Rage
Mega Drain
SolarBeam
Dragon Rage
Thunderbolt
Thunder
Earthquake
Fissure
Dig
Psychic
Teleport
Mimic
Double Team
Reflect
Bide
Metronome
Selfdestruct
Egg Bomb
Fire Blast
Swift
Skull Bash
Softboiled
Dream Eater
Sky Attack
Rest
Thunder Wave
Psywave
Explosion
Rock Slide
Tri Attack
Substitute
DynamicPunch
Headbutt
Curse
Rollout
Roar
Zap Cannon
Psych Up
Hidden Power
Sunny Day
Sweet Scent
Snore
Icy Wind
Protect
Rain Dance
Giga Drain
Endure
Frustration
Iron Tail
DragonBreath
Return
Shadow Ball
Mud-Slap
Ice Punch
Swagger
Sleep Talk
Sludge Bomb
Sandstorm
Defense Curl
ThunderPunch
Detect
Attract
Thief
Steel Wing
Fire Punch
Fury Cutter
Nightmare
Focus Punch
Dragon Claw
Water Pulse
Calm Mind
Hail
Bulk Up
Bullet Seed
Taunt
Light Screen
Safeguard
Brick Break
Shock Wave
Flamethrower
Rock Tomb
Aerial Ace
Torment
Facade
Secret Power
Skill Swap
Snatch
Overheat
Roost
Focus Blast
Energy Ball
False Swipe
Brine
Fling
Charge Beam
Dragon Pulse
Drain Punch
Will-O-Wisp
Silver Wind
Embargo
Shadow Claw
Payback
Recycle
Giga Impact
Rock Polish
Flash
Stone Edge
Avalanche
Gyro Ball
Stealth Rock
Captivate
Dark Pulse
X-Scissor
Natural Gift
Poison Jab
Grass Knot
Pluck
U-turn
Flash Cannon
Trick Room
HMs:
Cut
Fly
Surf
Strength
Defog
Whirlpool
Rock Smash
Waterfall
Rock Climb
Dive
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