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MathNet 2018-part-06 — 181 problems (EN–VI) Question 15

Math Olympiad Vault · MathNet 2018-part-06 — 181 problems (EN–VI)

Question 15

A skyscraper has 7 lifts, but each of them stops at only 6 floors. Nevertheless, for any two floors there is always a lift that connects the two floors directly.

Show that the skyscraper can have at most 14 floors, and that such a skyscraper with 14 floors can actually be realised.