Challenge Level

- If $k$ is an integer between 0 and 9, what possible values can $10k-k^2$ take? What are the minimum and maximum values?
- What do you know about the factors $k$, $k-1$ and $k+1$? What does this mean about the product of these three factors?
- What is $S$ in terms of $a$, $b$ and $c$? Make sure you read the question carefully!
- Can you use $S=N$ to write an equation involving $a$, $b$ and $c$?
- What values can $a$, $b$, $c$ take? What does the fact that $N$ is a 3-digit number tell us about $a$?
- Can you link the first parts of the question to the last part?
- Can you put bounds on the values of the parts of the equation involving $a$, $b$, and $c$?
- Can you rule out any values of $a$, $b$ or $c$?