Name: Gerard Who is asking: Teacher Level: All Question: Three fellows going to a Math Conference book into a motel. "That will be \$30.00" says the bellhop. Each fellow gives \$10.00 and they go off to their room. The manager enters and says "That was a \$25.00 room. Go and give them \$5.00 back."    The bellhop heads off but thinks....."how am I going to split \$5.00 between 3 fellows? Hey I will keep two dollars and give each guy a dollar." He does just that.......each fellow now paid \$9.00 and the bellhop kept two. 3 X 9= 27 plus the bellhops two = \$29.00 Where is the missing dollar? Hi Gerard I find this to be a fascinating problem because the logic seems so natural and correct but it's not. After the bellhop has given back three dollars, each mathematician has paid nine dollars for a total of \$27.00. You can see where the \$27.00 has gone, \$25.00 to the manager and \$2.00 to the bellhop. By adding the bellhop's \$2.00 to the \$27.00 that has been paid you are saying that the \$2.00 is in addition to the \$27.00 when, in fact, it is part of the \$27.00. I hope this helps, Harley

Go to Math Central