2016_Solutions_Grades 3-4-2016_Solutions_Levels

2016_Solutions_Levels_3&4

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The document provides solutions and explanations for the Math Kangaroo 2016 competition, specifically for Levels 3 and 4. Each problem is addressed with a clear step-by-step reasoning or calculation to derive the correct answer.<br /><br />1. In the first problem, Ernst's total is identified as the largest with a sum of 9.<br />2. The second problem discusses time periods of 8 weeks, 7 weeks, 2 days, and 5 days, concluding a total of 5 days remaining.<br />3. The third problem involves a sequence of numbers leading to the sum of 24.<br />4. Problem four focuses on a mirror image concept, explaining how images are reversed left-to-right.<br />5. The fifth problem identifies seat numbers between 61 and 80.<br />6. Problem six calculates that 6 people getting half an apple each results in needing 3 apples.<br />7. It describes how extending a shaded region can reveal a triangle.<br />8. Problem eight establishes a true statement that there are twice as many circles as triangles.<br />9. Problem nine calculates 2025 as the next year whose sum of digits equals 9, using divisibility by 9.<br />10. A maze problem concludes there are four different choices for the first move.<br /><br />Further problems employ logical or arithmetic solutions to deduce correct answers, such as calculating sums, evaluating spatial arrangements, pattern recognition, and using logical inferences about weights or ages. These explanations intend to help competitors grasp different mathematical concepts and problem-solving techniques applicable to each unique question posed during the Math Kangaroo 2016 contest. Each solution provides both the calculated answer and a rationale to support understanding, showcasing a variety of mathematical thinking and methodologies.

Keywords

Math Kangaroo 2016

Levels 3 and 4

problem-solving

step-by-step reasoning

mathematical concepts

sequence of numbers

mirror image

divisibility by 9

logical solutions

pattern recognition