The whole number are written across a piece of paper in order. There is room for 100 digits on each line and there are no spaces between each digit. What are the last 5 digits on the second line?
0123456789101112.......
single digit numbers:
10 of them
spaces needed: 10
double digit numbers:
90 of them
spaces needed 180
so the numbers from 0 - 99 require 190 spaces.
Starting in position 191 , we start writing 3 digits numbers.
So the remaining last 10 places of the second row would be
1001011021
making the last 5 digits of the second row
11021
you need 10 single digits (0123456...)
10 spaces
90 double digits
180 spaces
180+10=190
in 191, there are 3 digit #s
so it would be 100 101 102 1, or 1001011021, so the last 5 digits are 11021
To find the last 5 digits on the second line, we need to determine the number of digits on the first line.
The first line contains the numbers from 1 to 100, so there are 100 numbers with a maximum of 2 digits each. Therefore, the total number of digits on the first line is 100 x 2 = 200 digits.
Since each line can accommodate 100 digits, the first line fills up the first 100 digits of the second line. Therefore, the next 5 digits on the second line are the digits from 101 to 105.
Therefore, the last 5 digits on the second line are 01011.
To find the last 5 digits on the second line, we need to determine the range of digits that fall on the first line and calculate the last digit on the second line.
Given that there are room for 100 digits on each line, we can calculate the number of digits on the first line by finding the sum of an arithmetic series. The formula for the sum of an arithmetic series is:
Sn = (n/2)(a + l)
Where Sn is the sum of the series, n is the number of terms in the series, a is the first term, and l is the last term.
In this case, since the digits are written in order, the first term is 0 and the last term is 99.
Sn = (100/2)(0 + 99) = 50 * 99 = 4950
Therefore, there are 4950 digits on the first line.
Since there is room for 100 digits on each line, we can determine the line number where the first term of the second line appears by dividing the total number of digits by 100 and rounding up to the nearest whole number.
Line number = ceil(4950 / 100) = ceil(49.5) = 50
Hence, the first term of the second line appears on line number 50.
To find the last digit on the second line, we need to find the last term on the line. We can do this by subtracting the sum of digits on the first line from the total number of digits up to the last term on the first line.
Number of digits on the second line = 100 - (4950 - (99 + 1)) = 100 - (4950 - 100) = 100 - 4850 = 100 - 4800 = 50
Therefore, the second line consists of 50 digits, and the last 5 digits on the second line are the digits from the 46th to the 50th position on the line.
To get the actual digits, we can start counting from the first term of the second line, which is the 4851st term overall.
4851, 4852, 4853, 4854, 4855
So, the last 5 digits on the second line are 4851, 4852, 4853, 4854, 4855.