MathDB

8

Part of 2020 Durer Math Competition Finals

Problems(1)

integers 1, 2, 3, 4, 5,6 on a board, replace a,b with 4a - 2b

Source: 2020 Dürer Math Competition Finals Day2 E8 https://artofproblemsolving.com/community/c1622639_2020_

1/7/2022
The integers 1,2,3,4,51, 2, 3, 4, 5 and 66 are written on a board. You can perform the following kind of move: select two of the numbers, say aa and bb, such that 4a−2b4a - 2b is nonnegative; erase aa and bb, then write down 4a−2b4a - 2b on the board (hence replacing two of the numbers by just one). Continue performing such moves until only one number remains on the board. What is the smallest possible positive value of this last remaining number?
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