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Found problems: 1

2017 Israel Oral Olympiad, 7
Tags: combinatorics , combinatorics open , Arithmetic Progression , arithmetic sequence
The numbers $1,...,100$ are written on the board. Tzvi wants to colour $N$ numbers in blue, such that any arithmetic progression of length 10 consisting of numbers written on the board will contain blue number. What is the least possible value of $N$?