\n– The device writes 100 digits per minute for 30 minutes, so a total of 100 * 30 = 3000 digits are written.
\n– Natural numbers start from 1.
\n– Digits used for 1-digit numbers (1-9): 9 numbers * 1 digit\/number = 9 digits. (Numbers 1 to 9 completed)
\n– Digits used for 2-digit numbers (10-99): 90 numbers * 2 digits\/number = 180 digits. (Numbers 10 to 99 completed)
\n– Total digits used for 1-digit and 2-digit numbers = 9 + 180 = 189 digits. (Numbers 1 to 99 completed)
\n– Remaining digits to be written = 3000 – 189 = 2811 digits.
\n– These remaining digits are used for 3-digit numbers (100-999) and then 4-digit numbers (1000-…).
\n– Digits used for all 3-digit numbers (100-999): 900 numbers * 3 digits\/number = 2700 digits. (Numbers 100 to 999 completed)
\n– Total digits used for 1-digit, 2-digit, and 3-digit numbers = 189 + 2700 = 2889 digits. (Numbers 1 to 999 completed)
\n– Remaining digits = 3000 – 2889 = 111 digits.
\n– These 111 digits are used for writing 4-digit numbers (1000, 1001, …). Each 4-digit number uses 4 digits.
\n– The digits come from the sequence 1000, 1001, 1002, …
\n– Number of full 4-digit numbers whose digits are included in the 111 digits = floor(111 \/ 4) = 27 numbers.
\n– These 27 numbers are 1000, 1001, …, 1000 + (27 – 1) = 1026.
\n– Digits used for these 27 full 4-digit numbers = 27 * 4 = 108 digits.
\n– Total digits used so far = 2889 (up to 999) + 108 (for 1000 to 1026) = 2997 digits.
\n– The numbers written completely are 1, 2, …, 999, 1000, …, 1026.
\n– Remaining digits to reach 3000 = 3000 – 2997 = 3 digits.
\n– These 3 digits are the first three digits of the next number in the sequence, which is 1027.
\n– The digits of 1027 are 1, 0, 2, 7.
\n– The device writes the 2998th digit (‘1’ of 1027), the 2999th digit (‘0’ of 1027), and the 3000th digit (‘2’ of 1027).
\n– The device stops after writing the digit ‘2’ of the number 1027.
\n– The last number it was writing is 1027, and it is incomplete (only ‘102’ has been written).
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