Question

Clues:

1. it is a three-digit whole number.
2. it is divisible by 4.
3. it is divisible by 8.
4. it is not divisible by 5.
5. it is divisible by 9.
6. it is not divisible by 27.
7. it is divisible by 7.
8. it is greater than 500.
9. the sum of its digits is 9.
10 its ten digit is 0

Answer 1

From clues 1, 8, and 10, we know that the number looks like _0_. From clues 2, 3, and 6, we know that the number is divisible by 8 but not by 16 or 27, so the hundreds digit must be even and the last three digits must form a multiple of 8 that is not a multiple of 16 or 27. The only such multiple of 8 between 500 and 1000 whose digits sum to 9 is 864 which is not divisible by 5 but is divisible by 4, 8, 7, and 9. Therefore, the number is 860