# 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

In order to make it feasible for teachers to use these problems in their classwork, no solutions are publicly visible, so students cannot simply look up the answers. If you would like to view the solutions to these problems, you must have a Virtual Classroom subscription.## Similar Problems

### My Three Digits

I'm thinking of a three-digit number. The sum of my number's first and last digits is a perfect square. The sum of my number's first and second digits is also a perfect square. If my third digit is subtracted from my second digit, the result is 5. If my number is not a multiple of three, and it has no repeated digits, what is my number?

### Five Digit Number

The sum of the digits of a three digit number is eighteen. The first digit is three more than the last digit. There is a repeated digit in the number. What are all possible values of the number?

### Back to Back

X is a three-digit number. Y is the number obtained when the digits of X are reversed. Z is the six-digit number obtained by writing X and Y back to back, with X written first. W is the six-digit number obtained by writing Y and X back to back, with Y written first. What is the largest number which the sum of Z and W must be divisible by?

### Four Digit Number

I am a four digit number.

The sum of my digits is 20.

The product of my digits is 600.

The difference between my first two digits is 2, and the sum of my middle two digits is 11.

What number am I?

### Three Digits with Difference

I’m a three digit number, and the sum of my digits is 13. My first two digits differ by 3, and my last two digits differ by 5. What numbers could I be?

### Three Digit Number

I am thinking of a three-digit number. The sum of my digits is 17. Two of my digits add to 10, and two of my digits are the same. Find all possible values for my number.

### Three Digit Difference

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?

### Fiona's Telephone Number

When Shrek asks Fiona for her telephone number, Fiona is a bit coy about it, and tells Shrek the following information:

- My telephone number has 10 digits.
- There are no repeated digits in my telephone number.
- The first three digits are in ascending order.
- The second three digits are in descending order.
- Both the last four digits and the last two digits are multiples of sixty.
- My last four digits are not a multiple of 43.
- My first three digits are the square of an integer less than twenty.
- The sum of the second three digits is 14.

What number should Shrek dial?

### Grapes on the Vine

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?

### Two Digit Pattern Matching

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

- The digits are both multiples of three.
- Neither of the digits are multiples of two.
- The digits add to 8.
- The digits are perfect squares.