This is the 4917th most frequent French word.
savaient
"Did know" or "knew" (imperfect tense of "savoir").
In this sentence, 'savaient' (knew) is used to indicate that the children had knowledge about how to solve a problem in the past.
Les enfants savaient comment résoudre le problème.
The children knew how to solve the problem.
Here, 'savaient' expresses the repeated or constant knowledge of the location of their dog in the past.
Ils savaient toujours où trouver leur chien.
They always knew where to find their dog.
In this case, 'savions' (first-person plural form of 'savaient') is used to denote an understanding or awareness of a fact in the past.