What if ....
Someone was a bit nonchalant and did not back up his/her coins, but ... But he/she remembers his/her private key. Is there a way to 'restore' these 'lost' coins? IOW, is there a way to match private key and a specific address in the block-chain?
If you know the private key, then you can access the coins:
https://en.bitcoin.it/wiki/Private_keyJust as if you wrote the key down or printed it.
Thanks for this answer. The info reads:
The private key is mathematically related to the Bitcoin address, and is designed so that the Bitcoin address can be calculated from the private key, but importantly, the same cannot be done in reverse.
That's great. But, just to be sure, assume that I lost my wallet; completely, no back up. And all I do remember is my private key, can I restore (or recreate) the same wallet including all the coins?