math problem?

Question

How many 0's, 2's, and 7's are needed to write all of the integers from one to 2007?

Answer 1

I counted:

Zero is needed 506 times
Two is needed 609 times
Seven is needed 601 times

In the units place, the number 0 will appear every ten numbers (10, 20, 30, 40... up to 2000). That's 200 times
In the tens place, the number 0 will appear 10 times every hundred numbers (100, 101, 102, ..., 109, 200, 202, 202, ..., 209, ..., up to 2000, 2001, 2003, ..., 2007). Because it stops at 2007, that is 198 times (19 x 10 + 8).
In the hundreds place, the number 0 will appear 100 times every thousand numbers (1000, 1001, 1002, ..., 1099, 2000, 2001, 2002, ..., 2007) So this is 108 times.
In the thousdands place, you will never have a 0.

So adding it up, for zeros you have 200 + 198 + 108 = 506 times

Similar logic applies to 2:
In the units place, it appears every ten numbers for a total of 201 times (2, 12, ..., 2002).
In the tens place, it appears in 20, 21, 22, ... 120, 121, 122, ......., 1920, 1921, 1922, ... 1929). That's a total of 200 times.
In the hundreds place, it appears in 200, 201, 202, 203, ..., 299, 1200, 1201, 1202, ..., 1299). Again another total of 200 times.
Finally it appears in the thosands place for 2000, 2001, ..., 2007. That is 8 more times.

Adding it up for 2s you have 201 + 200 + 200 + 8 = 609 times.

Finally for 7:
Units (7, 17, 27, ..., 1997, 2007) = 201 times
Tens (70, 71, 72, ..., 79, 170, 171, ..., 179, 270, ..., 1970, ..., 1979) = 200 times.
Hundreds (700, 701, 702, ..., 799, 1700, 1701, 1702, ..., 1799) = 200 times.
Thousands = never.

So that's 201 + 200 + 200 = 601 times

And I've double-checked these numbers with an Excel spreadsheet.

0s = 506 times
2s = 609 times
7s = 601 times

Answer 2

Neat.

For all numbers from 000 to 999 (including leading zeroes), we need a total of 300 of each digit (for a total of 3000 digits).

Removing the leading zeroes...
3 for 000
18 for 001 to 009
90 for 010 to 099
Total 111 leading zeroes to remove.

So, for 1 to 999 we need
189 zeroes
300 twos
300 sevens.

For 1000 to 1999 there are no leasing zeroes to remove so we just add 300 of each.
So far we have 489 zeroes, 600 twos and 600 sevens.

For 2000, 2001, 2002, 2003, 2004, 2005, 2006 and 2007, we need to add 17 zeroes, 9 twos and a seven.

Answer:
506 zeroes
609 twos
601 sevens.

Answer 3

just gotta say that benoit3535's answer is wrong, i didn't figure it out but he started from 0, the problem says from one to 2007

Answer 4

Lots and lots...you are free to count them if you want