perplexus.info :: General : Miles to Kilometers

Miles to Kilometers (Posted on 2016-02-26)

Define F(N) = Min ((N- floor(N)), (ceil(N) – N))
Given that:
M miles = N kilometers, where M is a positive integer ≤ 2016 and N is a real number.

(I) Determine the value of M that yields the smallest value of F(N)
(II) What is the value of M yielding the next smallest value of F(N))?

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

quick Excel solution

| Comment 1 of 3

it is rather trivial to calculate F(N) for each integer value of M 1 to 2016, after doing that and sorting by F(N) (I used 1.60934 as my conversion factor M to N) I get the two smallest values for M = 1349 and 878

For M=1349, N=2170.99966 and F(N)=0.00034

for M=878, N=1413.00052 and F(N)=0.00052

Based on the definition of F(N), F(N) has a theoretical min of 0 and max of 0.5. Min happening when N is an integer and max when fractional part of N is 0.5

Within the given constraints, M=1788 gets really close to the theoretical max with N=2877.49992

Posted by Daniel on 2016-02-26 09:50:52

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