### 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.

### Basic Rhythms

Explore a number pattern which has the same symmetries in different bases.

### 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.

# Binary Squares

##### Stage: 5 Challenge Level:

Is there a general pattern of $1$'s and $0$'s in a binary number which is the square of a binary number containing only $1$'s? Try squares of $11$, $111$, $1111$ etc? To generalize you might use the fact that the sum of powers of two is a geometric series.