Question 18
Mauro wrote the list of numbers of $12$ digits with each digit equal to $0$ or $1$ such that the sum of digits in even positions is equal to the sum of digits in odd positions. Determine how many numbers are in Mauro's list.
CLARIFICATION: All numbers on the list have the first left digit equal to $1$.
CLARIFICATION: All numbers on the list have the first left digit equal to $1$.