The sum of 9 consecutive positive whole numbers is 2007. What is the difference between the largest and smallest of these numbers?
How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?
Consider a 10-digit number which contains only the numbers 1, 2 or 3. How many such numbers can you write so that every pair of adjacent digits differs by 1?