Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem14

11&12 Video Solutions 2011 problem14

Video Transcription

Video Summary

Paul entered integers into a 3x3 grid ensuring that each 2x2 square sums to 10. With four known numbers, the task is to determine if any given options represent the sum of the remaining five numbers. By analyzing and adding the equations representing each 2x2 square, and simplifying, we found the sum formula: \(20 - 3C = A + B + C + D + E\). This implies the final result divided by three should yield a remainder of two. Evaluating choices shows none satisfy this condition, leading to the conclusion that none of the provided options are correct.

Keywords

3x3 grid

2x2 square

sum formula

integer puzzle

remainder condition