Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

Video Summary

Sophia wants to arrange numbers 1 to 9 in regions of a shape so that the product of numbers in adjacent regions doesn't exceed 15. Key constraints focus on fixing 8, 9, and 1 in non-overlapping positions because they can only pair with 1. This allows for swapping, giving two possibilities. Similarly, 6 and 7 must be paired with 2, which provides four arrangements (due to their swappability and position). Remaining numbers 3, 4, and 5 allow for two configurations based on previous placements. Multiplying these possibilities results in a total of 16 valid configurations.

Keywords

number arrangement

product constraint

non-overlapping positions

valid configurations

swappability