Enigma 432: Holiday on the islands
19 January 2018
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From New Scientist #1582, 15th October 1987 [link]
Alan and Susan recently spent eight days among the six Oa-Oa islands, which are shown on the map as Os.
Only two of the islands, Moa-Moa and Noa-Noa, have names and hotels. The lines indicate the routes of the four arlines: Airways, Byair, Smoothflight and Transocean.
Alan and Susan started their holiday on the morning of the first day on Moa-Moa or Noa-Noa. On each of the eight days they would fly out to an unnamed island in the morning and then on to a named island in the afternoon and spend the night on that island. They each had eight airline tickets and each ticket was a single one-island-to-the next journey for two passengers. Alan had two Airways and six Byair tickets, while Susan had three Smoothflight and five Transocean tickets. They noticed that whatever island they were on, only one of them would have tickets for the flights out and so they agreed that, each time, that person should choose which airline to use.
Now Alan preferred that they should spend the nights on Moa-Moa, while Susan preferred Noa-Noa. However, they are an inseparable couple. So they each worked out the best strategy for the use of their tickets in order to spend the maximum number of nights on their favourite island.
How many nights did they spend on each island?