Hannah from Wallington High School for Girls suggested a possible starting point:

A strategy is to perhaps type in a number one by one so start with 1 then

2,3,4 etc and recording each light that gets turned on.

The Year 9 Puzzle Club at Huddersfield Grammar School worked out their machine's rules as follows:

We wrote down which lights lit up for numbers 1-45, then wrote down the sequences for each colour.

Yellow: 1, 11, 21, 31, 41...

Blue: 11, 22, 33, 44...

Green: 10, 21, 32, 43...

Red: 4, 10, 16, 22, 28...

Then we worked out the Nth term of each sequence.

Yellow: 10N+1

Blue: 11N

Green: 11N-1

Red: 6N-2

Dylan, from Landau Forte, told us his findings:

I found out that yellow started on 3 and I had to add 3 each time. All the numbers were a mixture of odd and even. Next, red started on 7 and I had to add 7 each time. The rule was all the numbers were a mixture of odd and even. Then blue started on 4 and I had to add 9 each time. The rule for this one was also that the numbers were odd and even. Finally green started on 3 and I had to add 4 each time. The rule for this was that all the numbers were odd.

Laurynne from Wallington pointed out that if the sequence has the rule $an+b$ with $a$ and $b$ both even, the terms will all be even, but if $a$ is even and $b$ is odd, the terms will all be odd.

Aswaath, from Garden International School, tested the machine in the same way, but gave us some extra interesting information about his machine's behaviour:

First, I experimented with the machine, and got these results:

From this I figured out the nth term of the pattern for each colour:

Green: 10n - 8

Blue: 12n - 2

Red: 3n + 2

Yellow: 12n - 12

From this I figured out all the numbers that made blue, yellow and green light up are even. The numbers for red are a mixture of odd and even as they increase by threes every time.

To take the the investigation further, I also recorded the results for various combinations of colours, in the table below:

From this I figured out the nth term of the pattern for the colour combinations:

Green + yellow: 60n - 48

Green + blue: 60n - 38

Green + red: 30n + 2

A strategy is to perhaps type in a number one by one so start with 1 then

2,3,4 etc and recording each light that gets turned on.

The Year 9 Puzzle Club at Huddersfield Grammar School worked out their machine's rules as follows:

We wrote down which lights lit up for numbers 1-45, then wrote down the sequences for each colour.

Yellow: 1, 11, 21, 31, 41...

Blue: 11, 22, 33, 44...

Green: 10, 21, 32, 43...

Red: 4, 10, 16, 22, 28...

Then we worked out the Nth term of each sequence.

Yellow: 10N+1

Blue: 11N

Green: 11N-1

Red: 6N-2

Dylan, from Landau Forte, told us his findings:

I found out that yellow started on 3 and I had to add 3 each time. All the numbers were a mixture of odd and even. Next, red started on 7 and I had to add 7 each time. The rule was all the numbers were a mixture of odd and even. Then blue started on 4 and I had to add 9 each time. The rule for this one was also that the numbers were odd and even. Finally green started on 3 and I had to add 4 each time. The rule for this was that all the numbers were odd.

Laurynne from Wallington pointed out that if the sequence has the rule $an+b$ with $a$ and $b$ both even, the terms will all be even, but if $a$ is even and $b$ is odd, the terms will all be odd.

Aswaath, from Garden International School, tested the machine in the same way, but gave us some extra interesting information about his machine's behaviour:

First, I experimented with the machine, and got these results:

Green | Blue | Red | Yellow |

2 | 10 | 5 | 0 |

12 | 22 | 8 | 12 |

22 | 34 | 11 | 24 |

32 | 46 | 14 | 36 |

42 | 58 | 17 | 48 |

52 | 70 | 20 | 60 |

... | ... | ... | ... |

From this I figured out the nth term of the pattern for each colour:

Green: 10n - 8

Blue: 12n - 2

Red: 3n + 2

Yellow: 12n - 12

From this I figured out all the numbers that made blue, yellow and green light up are even. The numbers for red are a mixture of odd and even as they increase by threes every time.

To take the the investigation further, I also recorded the results for various combinations of colours, in the table below:

G | B | R | Y | GY | GB | GR | BY | BR | RY | GYB | RGY |

2 | 10 | 5 | 0 | 12 | 22 | 32 | - | - | - | - | - |

12 | 22 | 8 | 12 | 72 | 82 | 62 | |||||

22 | 34 | 11 | 24 | 92 | |||||||

32 | 46 | 14 | 36 |

From this I figured out the nth term of the pattern for the colour combinations:

Green + yellow: 60n - 48

Green + blue: 60n - 38

Green + red: 30n + 2