1. Adela says all the numbers, except she skips the middle number in each consecutive group of three numbers. That is, Adela says 1, 3, 4, 6, 7, 9,..., 997, 999, 1000.
2. Becky says all of the numbers that Adela doesn't say, except she also skips the middle number in each consecutive group of three numbers.
3. Carina says all of the numbers that neither Adela nor Becky says, except she also skips the middle number in each consecutive group of three numbers.
4. Deidre says all of the numbers that none of Adela, Becky or Carina say, except she also skips the middle number in each consecutive group of three numbers.
5. Edith says all of the numbers that none of Adela, Becky, Carina or Deidre say, except she also skips the middle number in each consecutive group of three numbers.
6. Francine says all of the numbers that none of Adela, Becky, Carina, Deidre or Edith say, except she also skips the middle number in each consecutive group of three numbers.
7. Finally, Glen says the only number that no one else says.

Find nine single digit numbers (other than 1, 2, 3, ..., and 9) with a sum of 45 and a product of 9! (362,880).

For instance, 2, 2, 3, 4, 5, 6, 7, 8, 8 add up to 45, but their product is 645,120.

Try finding the answer without the use of a program.