Question 27
The integers from $1$ to $2002$, inclusive, are written on a board in increasing order $1$, $2$, $\ldots$, $2001$, $2002$. Then, those that occupy the first place, fourth place, seventh place, etc. are deleted, that is, those that occupy the places of the form $3k+1$.
In the new list, the numbers that are in the places of the form $3k+1$ are deleted. This process is repeated until all numbers are deleted from the list. What was the last number that was deleted?
In the new list, the numbers that are in the places of the form $3k+1$ are deleted. This process is repeated until all numbers are deleted from the list. What was the last number that was deleted?