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5

Part of 2016 Junior Regional Olympiad - FBH

Problems(3)

Junior Regional Olympiad - FBH 2016 Grade 6 Problem 5

Source:

9/29/2018
Pages of some book are numerated with numbers 11 to 100100. From the book several double pages were ripped out and sum of enumerations of that pages is equal to 49494949. How many double pages were ripped out?
number theory
Junior Regional Olympiad - FBH 2016 Grade 7 Problem 5

Source:

9/29/2018
In table https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvZC9hLzBjNjFlZWFjM2ZlOTQzMTk2YTdkMzQ2MjJiYzYyMWFlN2Y0ZGZlLnBuZw==&rn=dGFibGljYWEucG5n
1010 numbers are circled, in every row and every column exactly one. Prove that among them, there are at least two equal
tablecombinatorics
Junior Regional Olympiad - FBH 2016 Grade 8 Problem 5

Source:

9/29/2018
605605 spheres of same radius are divided in two parts. From one part, upright "pyramid" is made with square base. From the other part, upright "pyramid" is made with equilateral triangle base. Both "pyramids" are put together from equal numbers of sphere rows. Find number of spheres in every "pyramid"
geometry3D geometryspherepyramid