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Note that this "midpoint island" does not have to be one of the

Note that this "midpoint island" does not have to be one of the

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Island Nation is a country that prides itself in its organization. It consists of 100 equal square districts, laid out in a perfect 10x10 grid, with an island in the center of each of the 100 districts. The government of Island Nation wants to better connect the islands, building bridges in a straight line directly from one island to another. Consider five different islands. Suppose bridges are built between each possible pair of islands within these five. Prove that at least one of these bridges will be built directly over some island in the very middle of its path. Note that this "midpoint island" does not have to be one of the five islands that are having bridges built. (Hint: think of the "coordinates" of each of the islands as (r, y), where r and y are integers between 0 and 9.) 4.
Transcribed Image Text:Island Nation is a country that prides itself in its organization. It consists of 100 equal square districts, laid out in a perfect 10x10 grid, with an island in the center of each of the 100 districts. The government of Island Nation wants to better connect the islands, building bridges in a straight line directly from one island to another. Consider five different islands. Suppose bridges are built between each possible pair of islands within these five. Prove that at least one of these bridges will be built directly over some island in the very middle of its path. Note that this "midpoint island" does not have to be one of the five islands that are having bridges built. (Hint: think of the "coordinates" of each of the islands as (r, y), where r and y are integers between 0 and 9.) 4.
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