# "Sum of the digits of the numbers from 1-100"?

What does that mean?

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It's important to read the question carefully. It isn't asking you to add the *numbers* from 1 to 100. It is asking you to add up the *digits* used in writing the numbers 1 to 100.

You want to add up all the individual *digits* (not the value) used to make the numbers 1 to 100.

For example:

12 --> 1 + 2 = 3

37 --> 3 + 7 = 10

etc.

I will suggest a shortcut, however. Write the numbers in a big list going vertically. Let's add leading zeros to help line things up:

001

002

003

004

...

010

011

012

...

098

099

100

If you look at the hundreds column, you have only 1 digit to worry about:

Hundreds digits --> 1

If you look at the tens column, you have ten of each digit. So add up 0+1+2+3+...+8+9 and multiply it by 10:

Tens digits --> 10 * 45 = 450

Finally if you look at the ones column, you have ten of each digit again. So that's just like the tens column.

Ones digits --> 10 * 45 = 450

901

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• It means you add the digits in each number. For 1 digit numbers that is just the number, then for 2 digit number:

sum of digits in 10 = 1+0 = 1

sum of digits in 11 = 1+1 = 2

etc.

Probably the best way to do this is sum of all the units digits, then all the tens digits, (and then the single "hundreds" digit in 100) because there is a clear pattern to both the units digits and the tens digits.

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• It's 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + (1 + 0) + (1 + 1) + (! + 2) + (1 + 3) ... etc to + (9+ 9) + (! + 0 + 0)

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• Take all of the numbers between 1-100 and add them up. 1+2+3+4+5+6+7+8+9+10...+98+99+100

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• Anonymous
5 years ago

Yes, it means add up 1 + 2 + 3 + ... all the way up to 100

of course, it would behoove you to notice you can form 50 pairs of numbers that sum to 101:

1+100, 2+99, 3+98, all the way to 50+51

so to find the sum, you just calculate 50 * 101

Source(s): (department of work smarter, not harder)
• awesome method. Love the department name btw XD

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• 1 + 2 + ... + 8 + 9 + (1 + 0) + (! + 1) + (1 + 2) + ... + (9 + 8) + (9 + 9) + (1+0+0)

= (1*10) + (2*10) + (3*10) + ... + (9*10)]*2 +1

= (10 + 20 + 30 + ...+ 90)*2 +1

= 901

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