Coscott's solution seems incorrect for N=3. label 3 cars 1 is fastest, 2 is 2nd fastest 3 is slowest. There are 6 possible orderings for the cars on the road. These are shown with the cars appropriately clumped and the number of clumps associated with each ordering:
1 2 3 .. 3 clumps
1 32 .. 2 clumps
21 3 .. 2 clumps
2 31 .. 2 clumps
312 .. 1 clump
321 .. 1 clump
Find the mean number of clumps and it is 11/6 mean number of clumps. Coscott's solution gives 10/6.
Fix?
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