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Around the world

32 bytes removed, 08:11, 20 October 2010
Fix minor error (partial refill means tank not full afterward) Also change westbound to western etc to avoid confusion on return journeys.
A more detailed itinery follows. The times (T) are easy to calculate given that the time is always equal to the location of the main flight, and that all flights travel at the same speed.
*At T<nowiki>=</nowiki>0, main flight, westbound western primary assisting flight, and 1st westbound western secondary assisting flight begin westward journey.*At T<nowiki>=</nowiki>60, 1st westbound western secondary assisting flight refills westbound western primary assisting flight at D <nowiki>=</nowiki> 60.*At T<nowiki>=</nowiki>80, 2nd westbound western secondary assisting flight begins westward journey.*At T<nowiki>=</nowiki>100, westbound western primary assisting flight refills main flight at D <nowiki>=</nowiki> 100, giving it enough fuel to reach D <nowiki>=</nowiki> 280.*At T<nowiki>=</nowiki>120, 1st westbound western secondary assisting flight returns to base.*At T<nowiki>=</nowiki>140, 2nd westbound western secondary assisting flight partially refills returning westbound western primary assisting flight at D <nowiki>=</nowiki> 60.*At T<nowiki>=</nowiki>200, westbound western primary assisting flight and 2nd westbound western secondary assisting flight return to base.*At T<nowiki>=</nowiki>200, eastbound eastern primary assisting flight and eastbound eastern secondary assisting flight begin eastward journey.*At T<nowiki>=</nowiki>260, eastbound eastern secondary assisting flight refills eastbound eastern primary assisting flight at D <nowiki>=</nowiki> 300 (60 from 360).*At T<nowiki>=</nowiki>280, eastbound eastern primary assisting flight partially refills main flight at D <nowiki>=</nowiki> 280 (80 from 360).*At T<nowiki>=</nowiki>320, eastbound eastern secondary assisting flight returns to base.*At T<nowiki>=</nowiki>360, main flight and eastbound eastern primary assisting flight return to base.
This involves a total of six flights: one main, five returning. But by the time the eastbound eastern assisting flights have to depart, the westbound western assisting flights have returned to the island. So the same aeroplanes can be re-used for the eastbound eastern assisting flights, reducing the number of aeroplanes needed by two.
Therefore the puzzle can be solved with a total of four aeroplanes, including the main one. But certainly no fewer. Nothing is wasted in the above scenario, which confirms that it is the optimal solution. }}
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