Are you just working with these specific lists of 10 pairs and 10 triplets, or are these two lists just examples?

For these two lists, a brute force search would work pretty quickly. You know that you need at least four letters, so you could search all the possible choices of 4 letters from the 10 available. There are only 210 of these 4-letter choices, and you'll find a solution quickly, because there are a bunch of 4-letter choices that will work.

If the lists are variable, then this might not work so well. It depends on the constraints that are on the lists.