4. The numbers 20 and 21 are written on the board. Every minute, another number is written on the board, equal to the sum of any two of the already written numbers. Is it possible to eventually obtain the number $2020$ this way?
4. Answer: Yes, it is possible. Since the numbers 20 and 21 are already present on the board, we can obtain any number of the form 20a + 21b. Note that $2020=$ $101 * 20=(101-21) * 20+21 * 20=20 * 80+21 * 20$.

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