MathDB

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Part of 2017 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2017 Grade 6 Problem 1

Source:

9/19/2018
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"?
gamecardscombinatorics
Junior Regional Olympiad - FBH 2017 Grade 7 Problem 1

Source:

9/20/2018
Price of the book increased by 20%20\%, and then decreased by 10%10\%. How many percents should we decrease current price so we get a price which is 54%54\% percent of an original one?
percent
Junior Regional Olympiad - FBH 2017 Grade 8 Problem 1

Source:

9/20/2018
It is given function f(x)=3x−2f(x)=3x-2 a)a) Find g(x)g(x) if f(2x−g(x))=−3(1+2m)x+34f(2x-g(x))=-3(1+2m)x+34 b)b) Solve the equation: g(x)=4(m−1)x−4(m+1)g(x)=4(m-1)x-4(m+1), m∈Rm \in \mathbb{R}
algebrafunctionsfunctionfunctional equation