The numbers 1,2,...,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.(Karl Czakler) number theorygamecombinatorics