Puzzles and logic › Processes, invariants and strategy › Board operations and invariants
Product of the two final numbers
High school · ●●●○○ 50 pts
There are a total of 10040 numbers written on a blackboard: 2006 ones, 2007 twos, 2008 threes, 2009 fours and 2010 fives. Each operation erases four different numbers, one of each of four types, and writes one number of the fifth type (for example, erase one 1, one 2, one 3 and one 4, then write one 5; or erase one 2, one 3, one 4 and one 5, then write one 1). After a finite number of operations exactly two numbers remain on the blackboard. Find the product of these two numbers.