Recently, I found myself rotating between just a few different openings, so I decided to give this a shot. Rules are simple:
-must win with each opening once, within 4 attempts (if you can't win after 4 tries, move on)
-must rush relevant upgrades (elite ups, merc trainings, hero levels, rine trainings, etc.)
-must not be carried*

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All of these rules are basically to force you to use the unit - you can't just get the unit and leave it in your base the whole time, because you'll be behind. There is a * because some units are very difficult to carry with - if you used the unit and contributed to the victory, it counts.

You can, of course, do whatever you want after rushing the relevant upgrades. Can get spec/nix/os/whatever if you need to counter something, etc.

Great challenge not only for experienced players to switch it up, but for newer players to improve quickly. This will take anywhere from 47 games (win every game) to 188 games (lose every game).

I suggest going in some order that makes sense to make it easier to keep track of. For example, I'm doing all the elites first, in the order they appear in the cc. Next the heroes, then mercs, then rines.

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Examples/clarifications:
-Elite: get the maximum number of elites allowed (for example, 2 medi), get both elite ups for that elite from the cc, and re-buy the elite if it dies. There are 17 elites.

-Hero: straight-level the hero from 0 to 7 (max). There are 9 heroes.

-merc: get the merc+morph, get the 3x trainings and the ability asap, if there is one. There are 18 mercs (tanklings/cracklings and temples/warps are separate).

-marines: get the centershop ups asap (2 minors, major, ranges). Need to play 3 games (once with each major).

Oooo this is actually very fun Akash, my favorite is to try and win, while going 100% Pheonix, its very hard but possible. Definitely need some elites late game

All right Akash, I accept the challenge. I'll use your suggested order: Elites/Heroes/Mercs/Marines. Do you need replays uploaded for proof?

Hmm it'd be 47 replays which is a lot. Just a list would be nice, of how many attempts each one took.

You're free to post replays if you want though - I'll probably post mine once I finish for instructive/entertainment value :P

Finished! List of units/attempts below:

Clearly elites are my worst by far, while mercs/rines are my best
Will post replays in Guides section

Finished! Here's the list. Also, the satisfy the demands of TheTruth, here are my proofs of insurance, identity, and residence.

LOL well played sir
Impressive that nothing took you more than 2 attempts

Seering.

It was a fun challenge. It felt like a marathon. All those early games made me realize how many of the elites are total crap (diamondbacks, minimothership, science vessel, tanks).

Agreed. A lot of the elites are very situational and/or are terrible openings because they're too expensive. I find that the Diamondbacks are fun to use, but they are simply too expensive. $300 x2 + $350 + $300 for all their ups = $1250 just to get them fully useful. Other elites like Ghosts and Reapers are fully viable out-of-the-box and don't need a single upgrade to feed hard. This of course is why you see so many openings of Dustwings, Reapers, Ghosts, and even Ravens over units like Diamondbacks and Tanks. By the time you've got those units fully useful you're 4-5 army upgrades behind everyone else.