There are nine numbers between 1 and 100 that are divisible by 9 and whose digits also sum to 9.
Based on the provided reference, the 2-digit numbers between 1 and 100 that are divisible by 9 are: 18, 27, 36, 45, 54, 63, 72, 81, and 90. For each of these numbers, the sum of their digits is indeed 9, and all are divisible by 9. The reference specifically states that there are 9 such numbers. The question specifies numbers between 1 and 100, and since the reference identifies all such numbers satisfying the stated criteria, the answer is 9.
- Divisibility Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Here is a summary in a table format:
| Number | Divisible by 9 | Sum of Digits | Sum of Digits = 9 |
|---|---|---|---|
| 18 | Yes | 1 + 8 = 9 | Yes |
| 27 | Yes | 2 + 7 = 9 | Yes |
| 36 | Yes | 3 + 6 = 9 | Yes |
| 45 | Yes | 4 + 5 = 9 | Yes |
| 54 | Yes | 5 + 4 = 9 | Yes |
| 63 | Yes | 6 + 3 = 9 | Yes |
| 72 | Yes | 7 + 2 = 9 | Yes |
| 81 | Yes | 8 + 1 = 9 | Yes |
| 90 | Yes | 9 + 0 = 9 | Yes |
There are no other numbers between 1 and 100 meeting this criteria.
