My computer says there are =252 such numbers. Somebody will confirm it by using combinations such as:
9 nCr 3 * 3 =252 or maybe: (10 nCr 4 - 9 nCr 3) *2 =252......etc.
+658 case 1: there are 3 zeros.
- This one is pretty trivial, we know there are 9 of these numbers (1000, 2000, 3000... 8000, 9000)
case 2: there are 2 zeroes.
- All we need to do is find the number of such cases for the 1000s and multiply that for 9.
1001, 1002... 1008, 1009 there are 9 cases for which the the single digit is not zero
1010, 1020, ... 1080, 1090 there are 9 cases also.
Obviously there are also 9 cases for the non-zero hundreds digit cases.
So there are (9 + 9 + 9) * 9 = 243 for case 2.
So case 1 + case 2 = 252 such numbers, confirming guest's answer
