air kilometres but they cannot do more. Question 2 can be done by trial and error, but some hints may help the students approach the problem logically, for example, "Only two places need to be visited more than once. Which are they? Discuss your reasons." (These are Auckland and Rarotonga: Rarotonga because you must come back from Papeete, and Auckland because it is home and also, in the least air-kilometres itinerary, because it must be visited to get to Nuku'alofa.) Answers to Activity 1. a. Only two itineraries use up all the air points in one trip: either Auckland -- Nadi -- Honolulu -- Rarotonga -- Auckland or the reverse: Auckland -- Rarotonga -- Honolulu -- Nadi -- Auckland. b. Itineraries can include only a return trip to either Brisbane, Nadi, or Nuku'alofa. c. Answers will vary. The itinerary in a could be extended to include a return trip from Rarotonga to Papeete (2 284 km) or a return trip from Auckland to Nuku'alofa. Another itinerary could be a round trip taking in Brisbane, Osaka, and Nadi. 2. 35 897 air kilometres. The route that uses the least number of air kilometres is Auckland -- Brisbane -- Osaka -- Nadi -- Honolulu -- Rarotonga -- Papeete -- Rarotonga -- Auckland -- Nuku'alofa -- Auckland.