Its a cool idea but I would recommend A/B testing different GUI for picking numbers for removing some of the possible biases. I personally picked 7, most likel

Its a cool idea but I would recommend A/B testing different GUI for picking numbers for removing some of the possible biases. I personally picked 7, most likely because the human eye moves from top left to bottom right so I scanned what the choices were then picked the number near where my eye last looked. Also, I would love to see a heat map/click map of that page.