A very large book has pages numbered from 1 to 11521. How many times is the digit 3 printed?

4482

To find out how many times the digit 3 is printed in the page numbers of a large book with pages numbered from 1 to 11521, we can use a simple counting method.

Step 1: Identify the pattern
We need to identify the pattern first since it may help to simplify the counting process. In this case, we can observe that the numbers from 1 to 9 have the digit 3 once (3 itself), and the numbers from 10 to 99 also have the digit 3 once (in the tens place).

Step 2: Count the occurrences in each range
Now, let's break down the ranges and count how many times the digit 3 appears in each range:
- Range 1-9: This range contains only one-digit numbers, and there is one occurrence of the digit 3.
- Range 10-99: Here, each number has two digits, and the digit 3 appears in the tens place once. There are 90 numbers in this range, so the digit 3 appears 90 times in the tens place.
- Range 100-999: In this range, the digit 3 appears in the hundreds place, and there are 900 numbers (from 100 to 999). Therefore, the digit 3 appears 900 times in the hundreds place.
- Range 1000-11521: Here, the digit 3 appears in the thousands place. As there are 11,521 numbers in this range, the digit 3 appears 11,521 times in the thousands place.

Step 3: Calculate the total count
By adding up the occurrences in each range, we get:
1 occurrence (range 1-9) + 90 occurrences (range 10-99) + 900 occurrences (range 100-999) + 11,521 occurrences (range 1000-11521) = 13,512 times

Therefore, the digit 3 is printed 13,512 times in the page numbers of the very large book.

how many digit "3s" r there from 1-1,521?

A book has 500 pages numbered 1, 2, 3 and so on. How many times does the digit one appear in the page numbers?

I get 4502

counted using bash:

for i in `seq 1 11521` ; do echo $i ; done | tr -c -d '3' | wc -c

thx steve

die