Quote from: zatoichi on December 29, 2013, 08:29:21 PM

Doesn't the blockchain show where the new bitcoins are awarded?

No. The only information the blockchain has about where the bitcoins are awarded is the transaction outputs of the coinbase transaction. These outputs simply encumber some value(s) with a requirement of a digital signature from a particular private key (or set of private keys) to be reassigned elsewhere. There is no "node" information at all.

Quote from: zatoichi on December 29, 2013, 08:29:21 PM

Isn't the node a party to that transaction?

There are never any "nodes" that are party to any transactions. Transactions are a list of unspent outputs (as inputs to the transaction), a set of signatures providing proof that the transaction is authorized to spend those previously unspent outputs, and a list of new unspent outputs encumbered with a condition that must be met to spend those new unspent outputs (typically a signature from a private key that is associated with a bitcoin address). This is entirely "nodeless". Transactions are relayed from node to node with no knowledge of where they originated. The only difference with the coinbase transaction is that there is no list of previously unspent outputs or signatures, only new unspent outputs encumbered with the condition that must be met to pend them.

Quote from: zatoichi on December 29, 2013, 08:29:21 PM

If so, you should be able to get a minimum count (just remove duplicates).

Understand yet why there is no way to know how many nodes (or miners, or mining pools) exist?