Problems

Recognise it when: counting resources, such as N free slots, N connections, or "at most K at once".

free = threading.Semaphore(capacity)   # slots
items = threading.Semaphore(0)         # things to consume
mutex = threading.Lock()

# producer                 # consumer
free.acquire()             items.acquire()
with mutex: q.append(x)    with mutex: x = q.popleft()
items.release()            free.release()

Gotchas

• Unlike a Lock, any thread can release(). That's what makes hand-offs work.
• Order matters: acquire the semaphore before the mutex, or you deadlock.