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BG-MO 1990 Problem 1

    Consider the number obtained by writing the numbers 1,2,…,19901,2,\ldots,1990 one after another. In this number every digit on an even position is omitted; in the so obtained number, every digit on an odd position is omitted; then in the new number every digit on an even position is omitted, and so on. What will be the last remaining digit?

    Dataset text AI-MO AoPS. Quoted with source.

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