(a) Customers at a grocer's shop always want an integral number pounds of wheat, between 1 pound and 40 pounds. The grocer prefers to measure wheat in exactly one weighing with a beam balance. What is the least number of weights he needs?
(b) Customers come to a pawn shop with antiques. An antique always weighs an integral number of pounds, somewhere between 1 pound and 80 pounds. The owner of the pawn shop is free to do as many weighings as necessary to ascertain the unknown integral weight by using a beam balance. What is the least number of weights he needs?