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A Set Intersecting Every Arithmetic Progression

Source: Israeli Oral Olympiad #7

January 18, 2017
combinatoricscombinatorics openArithmetic Progressionarithmetic sequence

Problem Statement

The numbers 1,...,1001,...,100 are written on the board. Tzvi wants to colour NN 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 NN?
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