Quandaries and Queries


My name is Ernesto and I do not know how to solve this problem: The number 1 is written on a blackboard. After each second the number on the blackboard is increased by the sum of its digits. is it possible that at some moment the number 123456 will be written on the blackboard?
do I have to use remainders modulo 9?. Please help me


Hi ernesto,

You could use remainders modulo 9, but modulo 3 will also do:

Look at the remainders modulo 3 of the first few numbers you write down,
and ask yourself why this pattern should go on forever.