Question 42
In the blackboard are written some positive integers. We define the following movements:
(α) Every two successive numbers, say $n, n+1$, can be deleted by writing the number $n-2$.
(β) Every two numbers having difference 4, say $k, k+4$, can be deleted by writing the number $k-1$.
In the case we cannot apply any of the above movements the process finishes.
Determine the maximal possible value of the integer $c$ with the following property: Irrespectively with the numbers are written at the beginning in the table, at all process, all the numbers written in the table are greater than or equal to $c$.
(α) Every two successive numbers, say $n, n+1$, can be deleted by writing the number $n-2$.
(β) Every two numbers having difference 4, say $k, k+4$, can be deleted by writing the number $k-1$.
In the case we cannot apply any of the above movements the process finishes.
Determine the maximal possible value of the integer $c$ with the following property: Irrespectively with the numbers are written at the beginning in the table, at all process, all the numbers written in the table are greater than or equal to $c$.