The six states united against Qin, but they did not trust one another and the alliance soon fell apart.
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纵 means north-south. The six states lay in a line from 燕 in the north to 楚 in the south, so their union against 秦 in the west was 'vertical'. Qin's answer, 连横, paired it east-west with single states to break them apart. Together the two give 合纵连横.