It is quite frequent (and sometimes natural) to name callable classes as if they were functions.

Yes you should be reading instead of asking, it's easily found in the documentation.

That's mixing functions and classes naming conventions, but well, it's in line with the requested syntax (ugly to me)

I started with this way, however for testing that the node is the same memory object, we can just use id() built-in function.

Works for an arbitrary number of dices; may however miss the point of the kata.
Also, the count is performed at least twice per rule: not very clever.

Best solution so far, better than using collections.defaultdict as collections.Counter is explicitly made for this. Well done!

Agreed: filter lies in the paradigm of functional programming, and the proposed answers relies on count to keep some permanent state (in fact, modifying c counter, while filter does the looping).

So, while I find it clever, this solution is not easy to understand.

It does not work for you because you got newlines (\n) in your test string, that are not allowed by the rules of the kata.
Take care to use """....""".replace('\n', '') if you want to use such multi-line strings as long strings.

Untrue: len(walk) is not looping on walk, it accesses a parameter of list instance.

Moreover, looping over walk and counting the items would miss the optimization to directly reject a walk of wrong size, before even looking at the directions one after another.