Difference between revisions of "2020 IMO Problems/Problem 4"

(Created page with "Problem 4. There is an integer n > 1. There are n 2 stations on a slope of a mountain, all at different altitudes. Each of two cable car companies, A and B, operates k cable c...")
 
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Determine the smallest positive integer k for which one can guarantee that there are two stations
 
Determine the smallest positive integer k for which one can guarantee that there are two stations
 
that are linked by both companies
 
that are linked by both companies
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== Video solution ==
 +
https://www.youtube.com/watch?v=dTqwOoSfaAA [video covers all day 2 problems]

Revision as of 23:09, 12 October 2020

Problem 4. There is an integer n > 1. There are n 2 stations on a slope of a mountain, all at different altitudes. Each of two cable car companies, A and B, operates k cable cars; each cable car provides a transfer from one of the stations to a higher one (with no intermediate stops). The k cable cars of A have k different starting points and k different finishing points, and a cable car which starts higher also finishes higher. The same conditions hold for B. We say that two stations are linked by a company if one can start from the lower station and reach the higher one by using one or more cars of that company (no other movements between stations are allowed). Determine the smallest positive integer k for which one can guarantee that there are two stations that are linked by both companies

Video solution

https://www.youtube.com/watch?v=dTqwOoSfaAA [video covers all day 2 problems]

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