Grades 11-12 Video Solutions 2021-video 2021 11-12/14

Video Transcription

Video Summary

The problem involves arranging the first 1,000 positive integers to maximize odd sums of any three adjacent numbers. With 500 even and 500 odd numbers available, an odd sum occurs when three numbers include an odd number of odds. One effective pattern is repeating sequences of one odd and two evens, which consistently yields odd sums. This pattern uses 500 even numbers, accommodating 750 numbers in total, with 250 numbers remaining for grouping three odds, continuing the odd sum result. At the transition between patterns, one sum will be even, yielding a maximum of 997 odd sums. The answer is 997.

Keywords

odd sums

integer arrangement

odd and even numbers

pattern sequence

maximum odd sums