The sum of all 3-digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11, is _________

Find the sum of all 3-digit numbers $$n$$ such that $$100 \le n \le 500$$, $$11 | n$$, and $$n$$ contains no digit '1'.

1. List multiples of 11 in range: $$110, 121, 132, \dots, 495$$.
2. Filter by digit constraints:
   • 200s: 209, 220, 231 (X), 242, 253, 264, 275, 286, 297.
   • 300s: 308, 319 (X), 330, 341 (X), 352, 363, 374, 385, 396.
   • 400s: 407, 418 (X), 429, 440, 451 (X), 462, 473, 484, 495.
   • 500: 500 is not a multiple of 11.
3. Excluded numbers (containing '1'): 110-198 (all), 231, 319, 341, 418, 451.
4. Summing valid numbers:
   • Valid 200s: 209, 220, 242, 253, 264, 275, 286, 297.
   • Valid 300s: 308, 330, 352, 363, 374, 385, 396.
   • Valid 400s: 407, 429, 440, 462, 473, 484, 495.
   • Sum = 7744.

Correct Answer: 7744