1999_Solutions_Grades 3-4-1999_Solutions_Levels

1999_Solutions_Levels_3&4
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The document provides solution suggestions for the Math Kangaroo competition in the USA from 1999, specifically for students at Levels 3 and 4. Here's a summary of some of the solutions and their reasoning:<br /><br />1. **Fruit Counting (Q1)**: The solution involves counting the number of specific fruits — apples, oranges, and peaches — totaling 10 fruits.<br /><br />2. **Geometric Intersection (Q2)**: The problem illustrates the intersection area of four circles, highlighting visual clarity by coloring.<br /><br />3. **Cutting a Circle (Q3)**: To achieve 5 pieces from a circle, the solution indicates four cuts are needed, as each additional cut increases the number of pieces by one.<br /><br />4. **Age Difference (Q4)**: As a direct arithmetic problem, it discusses current ages and future ages where one person will be twice as old as another.<br /><br />5. **Distance Comparison (Q5)**: Two paths of right-angled turns cover the same overall distance regardless of path taken.<br /><br />6. **Distribution of Students (Q6)**: The students are divided into groups, and the total number of groups is calculated as 6 by dividing the total by the groups of boys and girls.<br /><br />7. **Balancing Scales (Q7)**: By balancing a known weight against an orange, the weight is determined to be 155g.<br /><br />8. **Tail Length (Q8)**: The full length of an origami figure's tail is doubled from its half-length measurement.<br /><br />9. **Day Calculation (Q9)**: The problem tracks days of the week, identifying a specific day through addition and modular arithmetic.<br /><br />10. **Sports Tournament (Q10)**: It calculates the minimal number of games to determine a winner, utilizing hypothetical perfect score conditions leading to a final match.<br /><br />11. **Arithmetic Correction (Q11-12)**: This involves correcting a mathematical mistake in scoring, concluding with the correct final result through arithmetic adjustment.<br /><br />Other problems cover a variety of mathematical principles, including multiplication patterns, volume calculations, logical reasoning, and basic algebra, demonstrating fundamental skills in arithmetic, geometry, and problem-solving typical of elementary mathematics competitions.
Keywords
Math Kangaroo
USA
competition
Levels 3 and 4
solutions
arithmetic
geometry
problem-solving
elementary mathematics
1999