Digital Equation

Age 16 to 18

Challenge Level Yellow star

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 $c$?

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