# Sum of Digits

Pro Problems > Math > Number and Quantity > Number Theory > Digits## Sum of Digits

Find the sum of all the integers between one and 100 which have 14 as the sum of their digits.

## Solution

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### I Have Three Digits

I am a three digit number, and the following things are true about me:

- The product of two of my digits is 8.
- The sum of my digits is 13.
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What number am I?

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_ _ _ x _ _ x _ =

What is the largest possible value you can create?

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The number of grapes on my grape vine is a three digit number. It is 7 times as much as the number of grapes on the vine last year, and 11 times the number of grapes on the vine the previous year. Next year, if I have twice as many grapes as I do this year, the number of grapes will still be a three digit number, but if I have three times as many grapes, the number of grapes will be a four digit number. If I have 21 times as many grapes, the number of grapes will be a five digit number.

If each jar of grape juice requires 20 grapes, how many full jars of grape juice can I make this year?

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I'm a three digit number. Reverse my digits and subtract, and the result is 198. Reverse my digits and add, and the result is 1272.

What number am I?

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### Two Digit Pattern Matching

How many two-digit numbers are there such that the digits match at least one of the following patterns:

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- Neither of the digits are multiples of two.
- The digits add to 8.
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Two positive integers, A and B, both have 3 digits. A is bigger than B. A – B is between 300 and 400. What is the value of A - B?

### All My Digits

All my digits are non-zero perfect squares. If you treat my first two digits as a two-digit number, and treat my last two digits as a two-digit number, the sum of these two numbers is also a perfect square. If I am a three digit number, what numbers could I be?

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I'm a three digit number. My first two digits multiply to 12, and my last two digits add to 14. What number am I?