Roma wrote on the board each of the numbers 2018,2019,2020, 100 times each. Let us denote by S(n) the sum of digits of positive integer n. In one action, Roma can choose any positive integer k and instead of any three numbers a,b,c written on the board write the numbers 2S(a+b)+k,2S(b+c)+k and 2S(c+a)+k. Can Roma after several such actions make 299 numbers on the board equal, and the last one differing from them by 1?Proposed by Oleksii Masalitin sum of digitsnumber theory