Episode 51 starts with the question from last time answered. While Basket was away, other players kept digging around Iron Island, and someone filled in the test pen to see where the slimes really spawn. They spawn in this one chunk. "So we can build a slime farm keeping in mind that this is the actual slime chunk here."
Following the cobblestone
First there are a couple of signs to read. "Looking for Diamonds or Danger? Go this way." Another says to follow the cobble markers to find some bling. Basket has a Fortune pick along, so Basket heads down a trail of cobblestone through the caves and past some lava. There are diamonds at the end, but Basket has no water bucket, no shield and no wood for torches, and the sword is a step down from the old one. "I really miss my better sword." Basket comes away with four diamonds and follows the cobblestone back to base.
The plan
Back on top of the farm, the torches come off. Basket wants the top to be spawnable for slimes and nothing else, so the lighting will go into a second layer above, built from light blocks set in a pattern. The slimes should hop off the corners into water, drown, and their slimeballs drop into the middle and down into the sorting system below. Only one chunk actually spawns slimes, but Basket might copy the same design onto every section so it all matches.
Testing in another world
Getting slimes to spawn on cue would be slow, so Basket builds a test platform in a separate world and uses spawn eggs. The slimes hop off in random directions and fall off the edges on their own, no trapdoors needed. With only one opening, a slime finds it eventually, though "not effectively." In water they do drown, but one hops right back out, which Basket didn't expect: "they could hop out possibly."
Redstone in a tight corner
Each corner gets a small water cubby where the slimes drown. Hoppers will pull the slimeballs out, and a dropper shoots them into the water channel so they fall into the system. Fitting a comparator, torches and repeaters into that space takes a few tries. The version that works loops on itself and burns out a redstone torch now and then, and Basket settles for it. "All right, I mean, this kind of works. Sure, sure, we'll do this."
Back in the test world, a big slime goes into water only two blocks deep to see if that's enough. It drowns. That means Basket can raise the whole thing one floor and use a flat layer of hoppers under two-deep water.
Orange it is
Then comes the look. Basket skips the darker blocks because they take ink sacs and asks chat for ideas. A viewer suggests orange. There's orange dye in a chest at the community center, and flowers bonemealed on a patch of dirt give more. With sand and gravel Basket makes concrete for the first time, tries it as powder and as solid concrete, and likes the concrete better. The pattern grows into rings around the middle, something like a bullseye. Glass will go on the sides so the slimes bounce off it and keep hopping until they drop into the water.
At the end Basket goes up high to look at it. "I think it looks pretty good." The same layout still has to go on the other sides, and maybe the other sections too. The video ends on the credits with no gameplay after them.