add digits of a naturals, in every move, sometimes on pair only
Source: IFYM - XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade,finals p4
November 13, 2022
number theoryDigitssum of digits
Problem Statement
A natural number is written on the board. In one move, we can take the number on the board and between any two of its digits in its decimal notation we can we put a sign , or we may not put it, then we calculate the obtained result and we write it on the board in place of . For example, from the number . we can get by , by , and by . Prove that no matter what is, we can reach a single digit number with at most moves.