According to Chris, there are 1449 combinations that are right.

There are 729 ways that each of the first two patterns can be formed and 81 ways for the third. However, there is overlap.

An *abcb* can be an *abac* if the *abcb*’s *a* = *c*. There are 81 ways.

An *abac* can be an *aabb* if the *abac*’s *a* = *b* and *a* = *c*. There are 9 ways.

An *abcb* can be an *aabb* if the *abcb*’s *a* = *b* and *b* = *c*. There are 9 ways.

A number can fit all three patterns if all digits are the same. There are 9 ways.

Adjusting for the overlaps, this gives the following:

*abac*? |
*abcb*? |
*aabb*? |
**Count** |

No |
No |
No |
N/A |

No |
No |
Yes |
72 |

No |
Yes |
No |
648 |

No |
Yes |
Yes |
0 |

Yes |
No |
No |
648 |

Yes |
No |
Yes |
0 |

Yes |
Yes |
No |
72 |

Yes |
Yes |
Yes |
9 |

Total: |
1449 |