### Code to Zero

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

### Binary Squares

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

### Learn about Number Bases

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.

# Basic Rhythms

##### Stage: 5 Challenge Level:

Notice the following pattern, written in base 10:

$$\begin{eqnarray} 987654321&=&8\times 123456789 &+&9\\ 98765432&=&8\times 12345678 &+&8 \\ 9876543&=&8\times 1234567 &+&7 \\ 987654&=&8\times 123456 &+&6\\ &\vdots & \\ 9&=&8\times 1&+&1 \end{eqnarray}$$

This patterns also holds in bases other than $10$. For example, in base $4$ we have $321 = 2 \times 123 + 3$, and so on.

Why is this the case?