Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Code to Zero

Why do this problem?

To beat the spies at their own game!

It gives practice in working systematically to consider all cases. First however you need to cut down the number of cases to be checked, so think about the relation between $a$, $b$ and $c$ and what you can deduce from it about the constraints on $a$, $b$ and $c$.

Possible approach

Ask the learners to find a relation between $a$, $b$ and $c$. Then have a class discussion about what can be deduced from this expression.

Key question

What do you know about $c^3-1$?

## You may also like

### Binary Squares

### Learn about Number Bases

Or search by topic

Age 16 to 18

Challenge Level

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

Why do this problem?

To beat the spies at their own game!

It gives practice in working systematically to consider all cases. First however you need to cut down the number of cases to be checked, so think about the relation between $a$, $b$ and $c$ and what you can deduce from it about the constraints on $a$, $b$ and $c$.

Possible approach

Ask the learners to find a relation between $a$, $b$ and $c$. Then have a class discussion about what can be deduced from this expression.

Key question

What do you know about $c^3-1$?

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.