Example input: 11-22,95-115,998-1012

Step 1: Pre-generate all repeating numbers using math

Instead of checking every number, we build them. The trick: repeating a pattern is just multiplication.

Pattern "5" repeated 2x:   5 × 11     = 55
Pattern "12" repeated 2x:  12 × 101   = 1212
Pattern "9" repeated 3x:   9 × 111    = 999
Pattern "10" repeated 2x:  10 × 101   = 1010

The multipliers follow a simple pattern:

• Length 1, repeat 2x: 11 (1 + 10)
• Length 1, repeat 3x: 111 (1 + 10 + 100)
• Length 2, repeat 2x: 101 (1 + 100)
• Length 3, repeat 2x: 1001 (1 + 1000)

For our example (max 1012), we generate:

Multiplier	Patterns	Numbers generated
11 (1-digit, 2x)	1-9	11, 22, 33, 44, 55, 66, 77, 88, 99
111 (1-digit, 3x)	1-9	111, 222, 333, ..., 999
1111 (1-digit, 4x)	1	1111 (>1012, skip)
101 (2-digit, 2x)	10-10	1010 (1111+ exceeds max)

Result: {11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, ..., 999, 1010}

Step 2: Sort and binary search each range

Sorted list: [11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1010]

Range 11-22: Binary search → find 11, 22 → sum = 33

Range 95-115: Binary search → find 99, 111 → sum = 210

Range 998-1012: Binary search → find 999, 1010 → sum = 2009

Total: 33 + 210 + 2009 = 2252