Is it possible to figure out cache size and associativity using the length of offset, index, tag fields?

I have a question where I am asked to find the size of a cache. I am given the following info:

a) the length of a memory address

b) the number of bits for offset, index, and tag fields.

I know I can use the numbers of bits to easily solve the line size and the number of sets. But as far as I know, there is no way for me to find the cache size without knowing the associativity, which we are not given.

Is there any way to find the associativity from the length of the memory address and the number of tag/index/offset bits?

Although it is tempting to assume the cache is direct mapped because we are not given associativity, the next question asks what the cache mapping scheme is and this prof is notoriously tricky, so I'm assuming there's more to it.