Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819

First rounding (up) yields: 546372820

2nd rounding (dn) yields: 546372800

3rd rounding (up) yields: 546373000

4th rounding (dn):546370000

5th rounding (up): 546400000

6th rounding (dn): 546000000

7th rounding (up): 550000000

8th rounding (dn): 500000000

Thanks for the challenge.

Linda, the Puzzlerz

as already mentioned above by savagegamer90 and Boiling Oil ... the sum of the remaining numerals after 4 round-offs is indeed 24

after 1st rounding - 473816950

after 2nd rounding - 473817000

after 3rd rounding - 473817000

after 4th rounding - 473820000

so 4+7+3+8+2=24