The Seven Cities Road
THERE is a strange road in Ozland called the Seven Cities Road. It is perfectly straight and runs from the town of Cellulite Valley through five other towns until it ends at the town of Negligee Junction.
Each of the seven towns is a whole number of kilometres down the road, with Cellulite Valley being at zero (0) kilometres. But what is strange is that the towns are so spaced that if you knew the distance travelled between any two towns on the road, you could determine the two particular towns uniquely.
In other words, the distance between any two towns on the road is unique.
What is the minimum distance between Cellulite Valley and Negligee Junction to make this possible, and assuming that this is the length of the Seven Cities Road, at what distances could the towns be along the road?
Here's my solution and/or comments :
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