Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem13

Levels 9&10 Video Solutions 2010 problem13

Video Transcription

Video Summary

The problem involves finding how many numbers have digits that sum to 2010 and a product of 2. The limitations allow using multiple 1's and only one 2 since the product of the digits must be 2. By setting one of the digits as 2, the rest must be 1's to satisfy the product condition. This results in having 2008 1's and one 2, summing up to 2010. The position of the 2 can vary among the 2009 digit positions. Therefore, the number of possible numbers is 2009, as the 2 can occupy any of these positions.

Keywords

digit sum

product condition

number positions

combinatorics

unique arrangements