# DFA for the set of strings of 0’s and 1’s such that there are two 0’s separated by a number of positions that is a multiple of 4

I've being trying to understand this statement for quite a long time especially the "number of positions" part, but i can't seem to interpret it correctly.What i understand is that the statement means that there should be two 0's seperated by a number of symbols that are multiples of 4 i-e (0 , 4 , 8 , 16...), according to my understanding the string "01110", should not be in the language as the 0's are seperated by three 1's which is clearly not a multiple of 4, but the solution to the problem i've seen here:

Suggests that "01110" is in the language.

Assuming you don't mind an NFA (getting a DFA is a bit fiddly, but obviously doable), you can fix the solution by removing the $(q_{4},0) \rightarrow q_{5}$ transition, and adding $(q_{5}, 0) \rightarrow q_{5}$ and $(q_{5}, 1) \rightarrow q_{5}$ transitions.