Smallest 4-digit lucky number, maths olympiad

Question

Let us call a positive integer "lucky" if its digits can be divided into two groups so that the sum of the digits in each group is the same. For example, 34175 is lucky because 3+7=4+1+5mfind the smallest 4-digit lucky number, whose neighbour is also a lucky number (i.e the integer next to it is a lucky number as well).

Answer 1

Smollest 4-digit lucky number is 1001(1+0 = 0+1) ,then next 4-digit lacky number is 1010 (1+0 = 1+0)