Adding another answer because I don't agree with the solutions proposed by cHao earlier - the analysis is fine.
First, why I disagree with the two solutions offered:
Reduce contention
Contention doesn't lead to deadlocks. It just causes poor performance. Deadlock means no performance whatsoever. Therefore, reducing contention does not solve deadlocks.
timeout on mutex.
A mutex protects a resource, and a thread locks the mutex because it needs the resource. With a timeout, you won't be able to acquire the resource, and your thread fails. Does it solve the deadlock problem? Only if the failing thread releases another resource that was blocking the other threads.
But in that case, there's a much better solution. Mutexes should have a partial ordering. If there is at least one thread that can both mutex A and B, you should decide whether A or B is acquired first, and then stick with that. This must be a transitive order: if you lock A before B, and B before C, then obviously you must lock A before C.
This is a perfect solution to deadlocks. Look back at the timeout example: it only works if the thread that times out waiting on A then releases its lock on B, to release another thread that was waiting on B. In the most simple case, that other thread was itself directly locking A. Thus, the mutexes A and B are not properly ordered. You should have consistently locked either A or B first.
The timeout case could also be the result of a cyclic order problem; one thread locks A then B, another B then C, and a third C then A, with the deadlock happening when each thread owns one lock. The solution again is the same; order the locks.
Alternatively said, mutex lock orders can be described by a directed graph. If a thread locks A before B, there's an arc from A to B. Deadlocks appear if the directed graph is cyclic, and then the arcs of that cycle are the deadlocked threads.
This theory can be a bit complex, but there are some simple insights to be found. For instance, from the graph theory, we know that trees are acyclic graphs. Hence, neither "leaf mutexes" (those that are always locked last) nor "root mutexes" (those that are always locked first) can cause deadlocks. Leaf mutexes are excluded because no thread ever blocks holding them, and root mutexes are excluded because the thread that holds them will be able to lock all subsequent mutexes in due time.