# 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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### 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?

### Three Digit Number

I'm thinking of a three-digit number. The sum of its digits is between 15 and 20 exclusive. The product of my first and last digits is 18. I don't have any repeated digits, and my digits are not in either ascending order or descending order. I am a multiple of three, but not of six. What number am I?

### 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.
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- The digits are perfect squares.

### 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.
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What number should Shrek dial?

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### The Middle Palindrome

If all the palindromes between 100 and 1000 were listed in order from smallest to largest, what is the average of the two numbers in the middle of the list?

NOTE: A palidrome is a number which reads the same forward and backward. For example, if you reverse the digits of 97279, you still have 97279.

### 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.
- My first digit is four times my second digit.

What number am I?

### Coffee Math

Johann was writing out a math problem when he spilled some coffee on his paper. The result was that some digits were covered up, as shown below.

♦7♦ + ♦♦9 ----- 50♦

If all but one of the hidden areas have the same digit, find all possible values for the sum of the hidden digits

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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?

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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?