MathDB

Peter and Basil play the following game on a horizontal table

1\times{2019}

. Initially Peter chooses

n

positive integers and writes them on a board. After that Basil puts a coin in one of the cells. Then at each move, Peter announces a number s among the numbers written on the board, and Basil needs to shift the coin by

s

cells, if it is possible: either to the left, or to the right, by his decision. In case it is not possible to shift the coin by

s

cells neither to the left, nor to the right, the coin stays in the current cell. Find the least

n

such that Peter can play so that the coin will visit all the cells, regardless of the way Basil plays.

Problem Statement