Roundoff Riddle

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.




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Sweet & very intelligent katty has 8 puppets(Jane Bird Barbie Angel Colleen Nora Lass Missy).
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* Nora has one puppet smaller on its left side
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* Missy has three puppets smaller on its right side

Also some puppets are inside the bigger puppets.

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