Milestones along a Road Trip
Number Theory
Level
1
Hank is on a 120 km road trip from Beihai to Beijing. There are several milestones along the way which follows these three rules:
- There are milestones at both the start and end points of the road.
- There are milestones at every fixed integer number of kilometers along the road.
- Every two neighboring milestones are at least 10 km away from each other.
Along his way, Hank spots a milestone marked 105 km.
How far apart are every two neighboring milestones, in kilometers?
The answer is 15.
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1 solution
Since there is a milestone at the start we know that there are two milestones one marked 120km away, another marked with 105km (we don''t know about the other ones). As we know Every two neighboring milestones are at least 10 km away from each other. By observation it can be concluded that it cannot take values 10,11,12,13,14.Hence the answer must be 15