This is modeled after <a href="indexa75c.html?topic=170.0" class="bbc_link" target="_blank">Clam Spammer's "skills you can't live without" challenge</a> for Lemmings-1 based games. Conceptually, you're focusing on minimizing the types of skills used and the number of one individual type of skill. I've no idea how fruitful this type of challenge will be for Lemmings 2. Hopefully it will still be fun and interesting.
Definition: The set of "skills you can't live without" on a level is the set of skills that is common to <strong>all <span class="bbc_u">gold</span> solutions</strong> to the level - without using every skill in this set, you can't possibly achieve gold on the level.
So for example, if you find a gold solution that uses only 1 roper, plus some number of builders and other skills, and another gold solution that uses only 1 builder, a few ropers, and a different bunch of other skills, the result for that level would be "1 roper, 1 builder". Your general approach would be to minimizing the number of <em>types</em> of skills to employ, finding as many disparate combinations of skill-types as you can. And then to minimize the number of skills used of a particular type, for each skill-type that appears to be common to all gold solutions.
Unlike Clam Spammer's challenge thread, I'm not including totals here, because different levels usually have fairly disparate types of skills, making the total not very meaningful.
I've started things off with a few results that are obvious enough for me to come up with at a glance.
(Note: <em>none</em> means there are no skills that are common to all gold solutions to the level. <em>no results reported</em> means no one has looked at the level yet to come up with any numbers.)
<span style="font-size: 0.7em;" class="bbc_size"><strong><span class="bbc_u">Classic</span></strong>
1: none
2: 4 builders
3: none
4: 3 builders, 1 basher, 1 miner
5: 1 blocker, 1 builder, 5 bashers, 1 miner, 1 digger
6: 1 builder
7: 2 builders, 1 digger
8: 1 builder, 2 bashers, 1 miner, 1 digger
9: 4 builders, 1 digger
10: 1 climber, 1 builder
<strong><span class="bbc_u">Beach</span></strong>
1: none
2: none
3: none
4: none
5: none
6: none
7: 2 platformers, 2 jumpers
8: none
9: none
10: 1 archer, 1 scooper
<strong><span class="bbc_u">Cavelems</span></strong>
1: none
2: 2 stompers, 3 scoopers
3: none
4: none
5: none
6: none
7: none
8: none
9: 3 platformers
10: 1 fencer, 1 platformer, 1 glue pourer, 1 stomper
<strong><span class="bbc_u">Circus</span></strong>
1: 1 climber, 1 jumper, 1 laser blaster, 1 glue pourer
2: none
3: 4 platformers
4: none
5: 1 platformer
6: 1 bomber
7: none
8: 1 platformer
9: 1 laser blaster, 1 platformer
10: none
<strong><span class="bbc_u">Egyptian</span></strong>
1: 1 digger
2: 1 glue pourer, 2 flamethrowers
3: none
4: 1 twister
5: 2 bashers, 1 stomper, 2 glue pourers
6: none
7: 1 laser blaster
8: 1 stomper, 1 platformer
9: 1 stomper, 1 basher
10: none
<strong><span class="bbc_u">Highland</span></strong>
1: 1 twister
2: none
3: 2 builders
4: 3 throwers
5: none
6: 2 ropers, 2 laser blasters
7: none
8: 1 basher, 1 laser blaster
9: 2 flamethrowers, 2 platformers, 1 attractor
10: none
<strong><span class="bbc_u">Medieval</span></strong>
1: 3 scoopers
2: none
3: none
4: 1 club basher, 1 sand pourer, 1 stacker, 2 glue pourers
5: 2 bombers, 1 builder, 1 club basher
6: 3 twisters, 1 platformer
7: none
8: none
9: none
10: none
<strong><span class="bbc_u">Outdoor</span></strong>
1: none
2: none
3: 1 platformer, 1 flamethrower
4: 1 glue pourer
5: none
6: none
7: none
8: 4 platformers
9: none
10: 1 platformer
<strong><span class="bbc_u">Polar</span></strong>
1: none
2: none
3: 1 roper
4: none
5: 1 roper
6: 1 stomper
7: none
8: 1 exploder
9: none
10: 2 glue pourers
<strong><span class="bbc_u">Shadow</span></strong>
1: <em>no results reported</em>
2: <em>no results reported</em>
3: <em>no results reported</em>
4: <em>no results reported</em>
5: <em>no results reported</em>
6: <em>no results reported</em>
7: <em>no results reported</em>
8: <em>no results reported</em>
9: <em>no results reported</em>
10: <em>no results reported</em>
<strong><span class="bbc_u">Space</span></strong>
1: none
2: 1 platformer
3: 1 platformer, 1 fencer, 1 stomper
4: none
5: 1 roper, 1 bomber
6: 1 filler, 1 shimmier, 1 climber, 1 spearer
7: none
8: 2 laser blasters
9: 1 ropers
10: 1 glue pourer, 1 jumper, 2 bazookas
<strong><span class="bbc_u">Sports</span></strong>
1: 3 flamethrowers, 1 bomber
2: none
3: 2 platformers
4: none
5: 2 stompers
6: 1 roper
7: 1 magno booter, 1 ballooner, 1 laser blaster, 1 platformer
8: none
9: 1 roper
10: 5 archers, 1 roper</span>