Question 32
Little Juku writes all integers from $1$ to $n$ on a blackboard, but as he does not know the digit $4$ yet, he skips all numbers that contain $4$. Juku's sister Mari erases two numbers on the blackboard and writes the absolute value of the difference of these numbers on the blackboard. Then Mari again erases two numbers on the blackboard and writes the absolute value of their difference on the blackboard, etc. Can it happen after a finite number of such steps that there are all integers from $1$ to $n$ that contain the digit $4$ and only these on the blackboard, each one exactly once, if
a. $n = 2021$;
b. $n = 10000$?
a. $n = 2021$;
b. $n = 10000$?