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Junior Regional Olympiad - FBH 2017 Grade 6 Problem 1

Source:

September 19, 2018
gamecardscombinatorics

Problem Statement

Lamija and Faris are playing the following game. Cards, which are numerated from 11 to 100100, are placed one next to other, starting from 11 to 100100. Now Faris picks every 77th card, and after that every card which contains number 77. After that Lamija picks from remaining cards ones divisible with 55, and after that cards which contain number 55. Who will have more cards and how many ? How would game end, if Lamija started with "55 rule" and Faris continues with "77 rule"?