Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Digital Equation

## You may also like

### Curvy Equation

### Euler's Totient Function

### Frosty the Snowman

Or search by topic

Age 16 to 18

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

- 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 $c$?

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.

How many numbers are there less than $n$ which have no common factors with $n$?

Frosty the Snowman is melting. Can you use your knowledge of differential equations to find out how his volume changes as he shrinks?