Grades 9-10 Video Solutions 2024-2024_9-10

Video Transcription

A number is written in each of the 12 circles shown. The number inside each square indicates the product of the numbers at its 4 vertices.  What is the product of the numbers in the 8 grey circles? If the products inside each square are a, b, c, d, and e, then we note that the required  product is a, b, d, divided by c squared, because dividing by c squared will divide away the double counting of the 4 white circles.  Then by simply calculating a, b, d, e over c squared, we get the correct answer of 40.

Video Summary

The problem involves determining the product of numbers in 8 grey circles positioned around several interconnected squares. Each square displays the product of its four vertex numbers. To find the product of the grey circle numbers, identify the products of numbers inside the squares (labeled a, b, c, d, and e in the problem). The key is to calculate \((a \cdot b \cdot d)/c^2\), which accounts for the double counting of the white circle numbers. By doing this calculation, you get the final answer of 40 as the product of the numbers in the grey circles.

Keywords

product calculation

grey circles

interconnected squares

vertex numbers

mathematical problem