The total number of vaults is a government secret and has been lost; there were the aforementioned "public" vaults, which numbered 122 and an undisclosed number of "private" vaults. Information on whether Vault-Tec was an international corporation or strictly U.S. based, cannot be released due to Vault-Tec and United States federal regulations. That said, Vault-Tec seems to have constructed some vaults in Canada. In a letter sent to a rejected D.C citizen the company offered to provide a list of "Vault-Tec facilities with available accommodations, in exciting locales such as Oklahoma and newly-annexed Canada."
Of the 122 known public vaults, only 17 were control, meaning that only 17 were made to public expectations. All others were designed to include a social experiment, sometimes with a select few of the inhabitants observing the occupants.