一道关于飞机加油的问题

问题：
每个飞机只有一个邮箱，飞机之间可以互相加油并且一箱油可供一架飞机绕地球飞半圈， 问为使至少一架飞机绕地球一圈飞回起飞的地方，至少需要出动几架飞机？ （所有飞机从同一机场起飞，而且必须安全返回机场，不允许中途降落，中间没有飞机场）


不知道这道题的正确解是多少，这里给出4架安排的方法。

为方便起见先给地球标上坐标。从起点开始自西向东分别标记为 0->1->2->3->4->5->0

plane A: from 0 to 1, oil = 1/2 - 1/6 = 2/6 when x = 1
plane B: from 0 to 1, oil=2/6 when x = 1

1/6 oil from B to A, now, plane A oil = 1/2, plane B oil = 1/6

plane B back to start point
plane A fly to x = 4

meanwhile

plane B from 0 to 5, oil = 2/6 at x = 5
plane C from 0 to 5, oil = 2/6 at x = 5

1/6 oil from B to C, now plane C has 3/6 oil and plane B has 1/6 oil

plane B back to start point
plane C from 5 to 4 with 2/6 oil at x = 4

at this point, plane C meets plane A

1/6 from C to A, now both A and C has 1/6 oil

meanwhile,
plane B and plane D starts from 0 and fly to x = 5
at x = 5, both B and D has 2/6 oil

also at x = 5, B and D meet A and C

B and D give 1/6 to A and C
and all of them can fly back to the start point



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I have no idea if we can do this with only three planes. It seems that the plane D is not fully used...