## You could count up a number of successes 

You can set a success cutoff number for each pool size, and just count all rolls equal or higher than that cutoff as successes and demand a given number of successes per pool as high or higher. This gets you around summing, you just look up success die.

To be honest, I think this is a horrible experience, because you essentially need to have a table at hand to remember the cutoffs, and it is not very exact either but here you go: 

|Pool| Cutoff |Successes Needed|Probability|
|:---:|:---:|:---:|:---:|
|1d12 |  12 | 1   |8.33% |     
|2d12 |  10 | 2   |6.25% |     
|3d12 |   9 | 3   |3.7% |     
|4d12 |  10 | 3   |4.69% |     
|5d12 |  12 | 2   |5.35% |