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To answer this question, you first need to find all the unique sets of 4 numbers that add up to 6. These are:

0006

0051

0042

0033

0411

0321

0222

3111

2211

Now we need to find which of these can be ordered to give numbers between 1111 and 9999:

0006: 6000

0051: 1500, 5001, 5010, 5100

0042: 2004, 2040, 2400, 4002, 4020, 4200

0033: 3003, 3030, 3300

0411: 1104, 1140, 1401, 1410, 4011, 4101, 4110

0321: 1203, 1230, 1302, 1320, 2013, 2031, 2103, 2130, 2301, 2310, 3012, 3021, 3102, 3120, 3201, 3210

0222: 2022, 2202, 2220

3111: 1113, 1131, 1311, 3111

2211: 1122, 1212, 1221, 2112, 2121, 2211

These are all the numbers between 1111 and 9999 with a digit sum of 6.

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