The parking lot for a local restaurant has 41 parking spaces, numbered consecutively from 0 to 40. Upon driving into this lot, a patron is assigned a parking space by the parking attendant who uses the hashing function h(k) = & mod 41, where k is the integer obtained from the last three digits on the patron's license plate. Further, to avoid a collision (where an occupied space might be assigned), when such a situation arises, the patron is directed to park in the next (consecutive) available space - where 0 is assumed to follow 40.
(a) Suppose that eight automobiles arrive as the restaurant opens. If the last three digits in the license plates for these eight patrons (in their order of arrival) are
206, 807, 137, 444, 617, 330, 465, 905,
respectively, which spaces are assigned to the drivers of these eight automobiles by the parking attendant?
b) Following the arrival of the eight patrons in part (a), and before any of the eight could leave, a ninth patron arrives with a license plate where the last three digits are 00x. If this patron is assigned to space 5, what is (are) the possible value(s) of x?