2025_Team_Competition_Solutions_Grades_11-12-2025 Team Competition Solutions Grades 11-12

2025 Team Competition Solutions Grades 11-12

Pdf Summary

This document is a solution key for the 2025 Math Kangaroo USA Team Competition for grades 11–12. It lists answers and brief explanations for 30 problems, covering a wide range of topics including geometry, algebra, combinatorics, number theory, and logical reasoning.<br /><br />Some recurring ideas in the solutions include:<br />- Using angle sums, symmetry, and geometric properties to find measures, areas, and shortest paths.<br />- Applying factorization and exponent matching to solve number theory problems.<br />- Counting carefully with inclusion-exclusion, arrangements, and casework in combinatorics.<br />- Recognizing patterns in sequences, recursive constructions, and transformations of equations.<br /><br />Examples of notable results:<br />- The largest angle in a triangle-like setup is 100°.<br />- A shortest surface path on a solid is 10.<br />- The minimum number of die rolls showing 6 is 10.<br />- The smallest solution to a transformed equation is 1/4.<br />- The minimum number of truth-tellers in a seating arrangement is 4.<br />- The number of distinct cube colorings using 6 of 9 colors, up to rotation, is 2520.<br />- The smallest possible number of kangaroos before a weight change is 7.<br />- The volume of water in a prism problem is 1296 ml.<br />- The largest number not representable as a sum of 6, 10, 15 and their multiples is 29.<br /><br />The short-answer section continues with counting and structure arguments, such as identifying the 44th number in a sequence, determining 12 valid values in a divisor-based problem, and solving a self-referential apples-and-plates puzzle, whose answer is 4.<br /><br />Overall, the document is a concise answer-and-explanation guide illustrating standard Kangaroo-style problem-solving techniques.

Keywords

Math Kangaroo

solution key

grade 11-12

geometry

algebra

combinatorics

number theory

logical reasoning

short-answer problems

problem-solving techniques