Question 4
Eight numbers, all zero, are written on a blackboard. A *move* consists in randomly selecting four of them, $a$, $b$, $c$, $d$, and replacing them by $a+3$, $b+3$, $c+2$ and $d+1$, respectively.
a) What is the smallest number of moves after which on the blackboard can appear eight consecutive numbers?
b) Is there a sequence of moves after which all the numbers on the blackboard are equal to $2015$?
a) What is the smallest number of moves after which on the blackboard can appear eight consecutive numbers?
b) Is there a sequence of moves after which all the numbers on the blackboard are equal to $2015$?