The everyone knows something principle is, in fact, quite useful in problem solving. Take a problem which has a numerical answer (e.g., how many pennies will fit into a 32 oz. bottle of Gatorade (sans fluid)?). Inquire of a statistically significant group of people. Collect their answers. Average them. You now have a good approximation as to the correct answer.

When solving Fermi problems, collective intelligence does surprisingly well.

I have, in fact, tried this with the pennies. The correct answer was around 1453; the collective intelligence of the 609th Information Warfare Squadron placed it at 1444; the closest individual guess was 1478.