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HMMT November 2016 H10

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We have 10 points on a line A1,A2⋯A10A_{1}, A_{2} \cdots A_{10} in that order. Initially there are nn chips on point A1A_{1}. Now we are allowed to perform two types of moves. Take two chips on AiA_{i}, remove them and place one chip on Ai+1A_{i+1}, or take two chips on Ai+1A_{i+1}, remove them, and place a chip on Ai+2A_{i+2} and AiA_{i}. Find the minimum possible value of nn such that it is possible to get a chip on A10A_{10} through a sequence of moves.

Dataset text NuminaMath olympiads. Quoted with source.

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