Grades 11-12 Video Solutions 2013-Levels 11&12 Video Solutions 2013 problem20

Levels 11&12 Video Solutions 2013 problem20

Video Transcription

Video Summary

Francois must pick 53 cards to ensure having three with the same digit sum. The cards are numbered from 100 to 999, each with unique numbers. By calculating possible digit sums from 2 to 26, each can appear at least three times among 900 cards. Using the pigeonhole principle, choosing 52 cards may allow digit sums to repeat at most twice without overlap. Thus, selecting an additional 53rd card guarantees a third card with the same digit sum as two others, satisfying Francois's condition.

Keywords

pigeonhole principle

digit sum

card selection

numbered cards

combinatorics