Question

I want to travel 1,000 miles on an adult tricycle and I have two spare tyres. However, I want to use all five tyres equally and have an equal mileage on each of the five tyres by the end of the trip. Of course I can only use three tyres at a time, so I will have to change tyres during the trip. At the end of the trip how many miles will each tyre have been used?

Answer 1

There are three tyres.  Each of them has to travel 1000 miles.  So a total of 3000 tyre miles is to be divided among 5 tyres.  Thus each tyre will be used  600 miles each  in the optimum solution.

Let us see one solution.  There may be more.

There are  tyres  a, b, c, d and e.

first 200 miles:    tyres  a,  b ,  c
next 200 miles:                      c,    d,  e
next 200 miles:            a,  b,        d
next 200 miles:            a.        c         e
next 200 miles:                b          d    e

Thus there are totally  8 tyre changes,  4 halts in between.