Question 54
The numbers $1, 2, \dots, 2020$ and $2021$ are written on a blackboard. The following operation is executed:
Two numbers are chosen, both are erased and replaced by the absolute value of their difference.
This operation is repeated until there is only one number left on the blackboard.
a) Show that $2021$ can be the final number on the blackboard.
b) Show that $2020$ cannot be the final number on the blackboard.
Two numbers are chosen, both are erased and replaced by the absolute value of their difference.
This operation is repeated until there is only one number left on the blackboard.
a) Show that $2021$ can be the final number on the blackboard.
b) Show that $2020$ cannot be the final number on the blackboard.