<P> To further illustrate why the riddle's sum does not relate to the actual sum, we can alter the riddle so that the discount on the room is extremely large . Consider the riddle in this form: </P> <P> Three people check into a hotel room . The clerk says the bill is $30, so each guest pays $10 . Later the clerk realizes the bill should only be $10 . To rectify this, he gives the bellhop $20 to return to the guests . On the way to the room, the bellhop realizes that he cannot divide the money equally . As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $6 and keep $2 as a tip for himself . Each guest got $6 back: so now each guest only paid $4; bringing the total paid to $12 . The bellhop has $2 . And $12 + $2 = $14 so, if the guests originally handed over $30, what happened to the remaining $16? </P> <P> Now it is more obvious that the question is silly . One cannot simply add a bunch of payments together and expect them to total an original amount of circulated cash . </P> <P> More economically, money is accounted by summing together all paid amounts (liabilities) with all money in one's possession (assets). That abstract formula holds regardless of the relative perspectives of the actors in this exchange . </P>

Riddle three friends go to a restaurant for lunch