Math Problem Statement
Water. Earth. Fire. Air. Long ago, the four nations lived together in harmony. Then, everything changed when the Fire Nation attacked. Only the Alex-tars, masters of all four elements, could stop them, but when the world needed them most, they vanished. A hundred years pass and you discover a group of 160 benders who can each bend at least one of the four elements: 124 can bend water, 113 can bend earth, 127 can bend fire, and 119 can bend air. Prove that there exist at least three Alex-tars in the group of 160 benders to restore peace and unity to the world!
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Set Theory
Inclusion-Exclusion Principle
Pigeonhole Principle
Formulas
Inclusion-Exclusion Formula
Pigeonhole Principle
Theorems
Inclusion-Exclusion Theorem
Pigeonhole Principle
Suitable Grade Level
Grades 10-12
Related Recommendation
Proving the Existence of Alex-tars: Using Inclusion-Exclusion and Pigeonhole Principle
Minimum Number of Students for 3 with Same Last Name Initial or Same Birth Day
Problem Solving: Division of a Sum Among Three Individuals
Solving School House Distribution and Travel Problem with Detailed Step-by-Step Solution
Counting Division Pathways for Five People with Social Distancing