Where can you find information about a 22 caliber rifle made by Firearms Int Washington DC serial B 175 56?
http://www.cornellpubs.com/Templates2/FI%201969.htm Look at the table of contents and see if you can find your rifle. Firearms International was an importer, not a manufacturer. They imported Sako, FN, Garcia, LaSalle, AYA, Rossi, Star, Astra, etc.
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What is the caliber of a ruger firearm with the serial number 31398342?
There is no way to determine the caliber of a firearm from the serial number unless you have access to detailed records from the company and this sort of information is seldom released to the public. However, almost anyone who is familiar with firearms could probably answer this question by looking at the gun. If not, a gunsmith can take an exact measurement.