1981 USAMO 第 2 题

What is the largest number of towns that can meet the following criteria. Each pair is directly linked by just one of air, bus or train. At least one pair is linked by air, at least one pair by bus and at least one pair by train. No town has an air link, a bus link and a train link. No three towns, $A, B, C$ are such that the links between $AB, AC$ and $BC$ are all air, all bus or all train.

满足以下条件的城镇数量最多是多少？每对航班、巴士或火车均直接相连。至少一对通过飞机连接，至少一对通过公共汽车连接，至少一对通过火车连接。没有一个城镇拥有航空线路、巴士线路和火车线路。没有三个城镇$A、B、C$ 之间的联系全部是航空、全部公共汽车或全部火车。