Grades 11-12 Video Solutions 2015-Levels 11&12 Video Solutions 2007 part3

Video Transcription

Video Summary

The video transcript explores a variety of mathematical questions with detailed solutions. <br /><br />Question 21 discusses how to determine the number of different colors needed for marbles, each distinguished by the unique sum of their digits. The solution reveals 28 different colors are required.<br /><br />Question 22 hinges on identifying truth values of statements, primarily logical reasoning and deduction of statement interdependencies, concluding that statement D is the first true statement.<br /><br />Question 23 asks about coloring the edges of a cube using four distinct colors, such that each face contains all four colors. The problem involves combinatorial arrangements, finally determining there are 48 ways to achieve this.<br /><br />Question 24 addresses how many regular polygons exist such that the measure of each interior angle is an integer. This boils down to factoring numbers and ensuring angle divisibility rules, concluding that 22 different polygons exist.<br /><br />Question 25 involves permutations of powers of 2 and the notion of constructing three-digit positive integers. It involves combinatorics and concludes with finding five suitable configurations.<br /><br />Question 26 asks for the count of right triangles with a specific side and integer legs possible. Four configurations are possible by leveraging inequalities and integer restrictions.<br /><br />Question 27 involves ratio calculation between the quadrilateral formed by consecutive midpoints of a rectangle and the entire rectangle, utilizing coordinate geometry approaches to find a ratio of 7/32.<br /><br />Question 28 considers solving a word problem involving logic and algebra concerning rectangles alongside specific conditions. The solution relies on eliminating impossibilities and repeated logical constraints, concluding that there are three blue rectangles.<br /><br />Question 29 utilizes a number elimination problem with cyclical counting, involving pattern recognition and modulus operations to find that 65 is the first number by the last standing participant.<br /><br />Question 30 aims to balance replacements in spelling "Kangaroo" with digits to find overlapping divisions by 11 conditions, resulting in the common digit "5" between two players' configurations.

Keywords

mathematical questions

digit sums

logical reasoning

cube coloring

regular polygons

permutations

right triangles

coordinate geometry

word problem

number elimination