# Place Value Stage 4 - Short Problems

### Weekly Problem 9 - 2008

##### Stage: 3 and 4 Challenge Level:

The sum of 9 consecutive positive whole numbers is 2007. What is the difference between the largest and smallest of these numbers?

### Weekly Problem 33 - 2010

##### Stage: 3 Short Challenge Level:

How many positive integers $n$ exist for which $n^2$ has the same number of digits as $n^3$?

### Weekly Problem 46 - 2010

##### Stage: 3 Short Challenge Level:

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?