Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem28

Levels 9&10 Video Solutions 2010 problem28

Video Transcription

Video Summary

The problem involves finding three-digit numbers where the middle digit is the arithmetic mean of the other two digits. Digits A, B, and C form the number ABC, subject to the condition \(2B = A + C\). By evaluating cases for \(B\) from 1 to 9, you find different possibilities for A and C. The number of valid numbers for \(B = 1\) is 2, \(B = 2\) is 4, \(B = 3\) is 6, \(B = 4\) is 8, \(B = 5\) is 9, \(B = 6\) is 7, \(B = 7\) is 5, \(B = 8\) is 3, and \(B = 9\) is 1. Summing these gives a total of 45 such numbers.

Keywords

three-digit numbers

arithmetic mean

digit conditions

valid numbers

number combinations