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I think there should be new tutors, because some moves that can be tutored in gen IV have pokemon that can level up from it in a small amount. I am going to list the move, how many pokemon can level from it, haw many pokemon can learn it through breeding, max tutor #, and its current tutor generation #. This is based off of veekun.com for official pokemon. You might be surprised.

Mega Punch, lvl: 4, egg: 2, max: 118, III
Mega Kick, lvl: 1, egg: 0, max: 118, III
Metronome, lvl: 6, egg: 4, max: 54, III
Mimic, lvl: 6, egg: 3, max: 372, III
Seismic Toss, lvl: 9, egg: 2, max: 127, III
Dynamic Punch, lvl: 5, egg: 6, max: 125, III
Snore, lvl: 10, egg: 11, max: 485, IV
Draco Meteor, lvl: 0, egg: 0, max: 20, IV
Air Cutter, lvl: 5, egg: 1, max: 66, IV
Ominous Wind, lvl: 10, egg: 3, max: 85, IV
Trick, lvl: 7, egg: 8, max: 77, IV
Vacuum Wave, lvl: 2, egg: 3, max: 27, IV
Spite, lvl: 10, egg: 9, max: 76, IV
Gastro Acid, lvl: 9, egg: 0, max: 16, IV
Gunk Shot, lvl: 7, egg: 0, max: 33, IV
Heat Wave, lvl: 5, egg: 5, max: 66, IV
Iron Head, lvl: 11, egg: 4, max: 65, IV
Outrage, lvl: 5, egg: 3, max: 53, IV
Seed Bomb, lvl: 5, egg: 4, max: 53, IV
Superpower, lvl: 12, egg: 3, max: 64, IV

I could have asked for ALOT more than these. But I wanted it to be an even and reasonable #. What do you guys think?
Bolded ones are ones that ABSOLUTLY NEED a place, no questions asked.