2017_Solutions_Grades 5-6-2017_Solutions_Levels

2017_Solutions_Levels_5&6

Pdf Summary

The document is a solution guide for the Math Kangaroo 2017 competition, specifically for problems 1-30. Each problem is followed by the correct answer, an explanation of the reasoning behind it, and sometimes additional background math to support the solution. The problems cover a range of math topics and skills including basic arithmetic, logic puzzles, geometry, and number theory. <br /><br />Highlights include:<br /><br />- Problem 1 involves determining which set of cards cannot be rearranged into its original order by a single swap.<br />- In Problem 2, readers work through a problem involving animals and counting legs to find the solution.<br />- Problem 3 involves patterns and coverage of a rectangle, explaining why one option cannot be completely covered.<br />- Problem 7 involves symmetry and is solved by calculating the sums of pairs of numbers.<br />- Problem 12 uses logic and pattern recognition to deduce a padlock's combination by matching letters with numbers.<br />- Problem 18 involves optimization and deduction to maximize the final monetary gain from a series of transactions.<br />- Problem 23 deals with permutations and calculates steps needed for rearrangements using specific conditions.<br />- Problem 29 covers arrangements of colors on a map such that no adjacent countries share the same color using a standard four-color theorem approach.<br />- The solutions use varied approaches, including algebra, visualization, symmetry, and permutation analysis to arrive at the correct answers.<br /><br />The guide serves as a comprehensive solution resource for students and instructors preparing for or reviewing the Math Kangaroo 2017 competition, providing not only the solutions but also the logical structure to solve similar problems.

Keywords

Math Kangaroo 2017

solution guide

arithmetic

logic puzzles

geometry

number theory

permutations

symmetry

pattern recognition

four-color theorem