Three would be my answer, too, but wondering how subsequent visitors would go on. It could get very difficult by following that rule.
I've got another 'keen'... Ouch!
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Post-lockdown a gransnetter was invited to go to an exclusive event with vast quantities of gin, cake, famous hairdressers to deal with 'isolation hair', and a wodge of money for each guest. The only catch was she had to guess the password to get in. She waited by the door and listened. Another guest arrived, knocked on the door and the doorman said, "twelve." The guest replied, "six " and was let in. A second guest came to the door and the doorman said, "six." The guest replied, "three" and was let in. The gransnetter thought she had heard enough and walked up to the door. The doorman said ,"ten" and she confidently replied, "five." But she was not let in. What should she have said? Can you help her get in? 
Oh, we did! Sorry! 
It is as many of you guessed: three! The number of letters in the word 
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