Question 28
Višnja decided to write all integers from $1$ to $2014$ on a board in some order. Her brother Marijan will write the absolute value of the difference of each pair of adjacent numbers, and then erase the previously written numbers. Marijan will repeat this procedure until there is only one number left on the board. Determine the largest possible value of the number that will remain on the board.
(Estonia 2012)
(Estonia 2012)