Any mob trap within 16 blocks of the bottom of the map will catch slimes as well, but you have to be careful to not hurt the slimes too much to get them to split the most. Punching and drowning are the safest ways to ensure that they'll split into more slimes. Also, you want a large room so that bigger slimes will spawn which can then have more splits.
The most important thing besides the depth is that it's in a chunk suitable for slimes. Slimes can only spawn in 10% of the chunks, picked randomly depending on the seed. You can calculate which chunks are suitable with this tool by trunkz though: http://www.minecraftforum.net/topic/397835-find-slime-spawning-chunks/
They only spawn a tenth as often as other mobs, but they'll also spawn in any light level, so if you're digging for diamonds at bedrock level, you'll usually find quite a few naturally.
Let's do some experiments!
I'm going to assume we're interested in making square holes, for several reasons:
- It's easier to measure and compare that way.
- You probably want flat walls.
- If you find a good blast pattern, you can do the same thing side-by-side to clear a larger area in multiples of the pattern without wasting any blast power.
I am also going to ignore the possibility of encountering a vein of dirt or gravel, which is much easier to blast and results in much less predictability of the results due to irregular obscured shape.
That 3×3×3 cube fact is true, but only if the TNT is actually fully encased — which would be a waste of time since you would have to light the TNT and then plug the hole. The way I have used TNT to dig is to make a 3-deep hole and place TNT at the bottom of it (or drop lit TNT down from the top, which requires less careful cursor work). In addition to blowing out the cube, it will also take out nearly all of the fourth layer above (say, with one block remaining). I have found this to be a very convenient strategy.
In this case, each TNT will blow up 3×3×4 - 3 - 1 = 32 blocks, and 4 (11%) were removed by hand.
Suppose we place a single TNT on a flat stone surface and ignite it. I did this and got a 7×1×7 hole where the outside was only partly exploded, leaving 12-15 blocks [3 trials].
7 × 7 - 14 = 35 blocks, and you'll want to clear the remaining 14 (28%) by hand since they're irregularly shaped so a blast would be wasteful.
How about the same as above but with the TNT inset into the ground by 1 block? That turns out to be the same as the first case without the blocks above, so it removes only 9+8 = 17 blocks.
Let's go higher. Placing a TNT on top of some leaves (blast resistance = 1) results in another 7×7 pattern, but with only 9 blocks left unexploded.
Another block higher and there are many more blocks remaining; I'll stop here for now and assume this direction isn't useful.
So, the on-the-surface configuration blasts more area, but surely it wastes all that blast going sideways and upward. Let's try setting off a TNT in the center of a 3×3×4 hole produced by the first method (supporting the TNT with a block of leaves).
Whee! The second blast nearly perfectly enlarged the cube, leaving only 4 corner pieces. That means we destroyed 5×5×5 - 4 = 121 blocks, or 60.5 per TNT, with 3 + 4 = 7 blocks (6%) to clear by hand.
A third TNT, supported 2 spaces above with 1 block of leaves, after clearing the irregularities, resulted in an irregular 7×7×6 hole with 52 blocks left in it, meaning 7×7×6 - 52 - 7 = 235 blocks = 78.3̅ per TNT were destroyed. This is an excellent efficiency, but notice that the amount of hand-work has gone up to 59 blocks (20%).
A fourth centered blast, after clearing the irregularities, only scarred the walls a bit; I'm not going to bother working out the numbers.
In conclusion, based on the patterns I've tried, the most efficient pattern (in terms of blocks exploded per block of TNT) is three blasts at the same center point, starting with a 3-deep hole in the ground, manually smoothing off the walls between each step.
(However, these tests were conducted in creative mode, so I did not concern myself with safety (i.e. getting out of the hole). The temporary stairs required to exit after the second and third setups may affect the patterns; or you could use a water stream or drop lit TNT from a frame above.)
On the other hand, if you want to minimize manual effort while making a square hole, then I recommend using two blasts, as that has the lowest manual work percentage while still being quite efficient in TNT.
My experimental setup was a flat stone surface with a surrounding 11×11 obsidian ring to aid counting and provide a height reference in case I blew up all the surface. Shown here is the situation immediately after the fourth blast discussed above.
Also, thanks for asking this question! I have learned an improvement to my own blasting technique.
Best Answer
To my knowledge (and experience), you can farm squid by having an aquarium. I had a 4*4*4 farm, which basically: