Challenge Level

There was a great deal in this problem and James has answered part of it:

Using only three rods with each one not exceeding 10 you can add and minus the following numbers which can go from 1-13.

The three numbers are 9, 3 and 1.

1 | = | 1 |

2 | = | 3-1 |

3 | = | 3 |

4 | = | 3+1 |

5 | = | 9-3-1 |

6 | = | 9-3 |

7 | = | 9-3+1 |

8 | = | 9-1 |

9 | = | 9 |

10 | = | 9+1 |

11 | = | 9+3-1 |

12 | = | 9+3 |

13 | = | 9+3+1! |

Well done James. Is 13 the largest number and why?

Can any of you help with some of the rest of the question:

In how many ways can you make 10?

What is the maximum number you can make with 4 rods?

Perhaps you can send in some more ideas.