Ruger has sn data on their web site.
Ruger's website has a sn function.
It was manufactured in 1961.
If the Ruger website is working, it has sn data on it.
Ruger will tell you if you phone customer service.
Ruger's website has extensive sn data. 75-175 or so
Blue Book of Gun Values
Ruger's website has a serial number look up function you can use.
If you go to the Ruger website, look under customer service, then historical documents, then rifle, and Model 77, there is a serial number list by year.
The Ruger website, under customer service, historical data, pistols, will list the serial number ranges for each year of manufacture. Get the serial number, and hunt it down. Good luck.
Ruger's website has extensive serial number data.