In other words, Page and Brin asked Armstrong to interview himself in front of them.
"So I said, 'Look, I'm a very direct person, very honest. Here's what I would ask, the following questions,'" he recalls.
"I thought that was interesting," Armstrong says about the unorthodox interview.
Over the next decade, Armstrong became an important player in Google's exponential growth, including spearheading the company's AdSense division. After holding multiple C-level positions, he left the company in 2009 to lead AOL.
Armstrong wasn't the only one the Google co-founders used this tactic on.
"I realized later, after working with them, that that was not an anomaly," he said. "That was one of their tactics."
Google has long held a reputation for its difficult interviews. In the past, candidates had to wrangle with brainteaser questions such as, "How many times a day does a clock's hands overlap?" and, "Estimate how many gas stations there are in Manhattan."
Hiring managers have since moved on to asking behavioral questions such as, "Describe a time when you solved a difficult problem," which they've found to be better predictors of on-the-job success.
But while Google job applicants are less likely to have to figure out impossible scenarios on the spot, they might want to take a few minutes to mentally prepare for a curveball question, including the interview question you would ask yourself.
Check out the one interview question this IBM exec asks every applicant.