# I Have Three Digits

Pro Problems > Math > Number and Quantity > Number Theory > Digits## 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?

## 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

### 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?

### 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.

### 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

### 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?

### Palindrome Addition

Find the smallest positive integer which must be added to 30504 so that the resulting number is a palindrome.

Note: a palindrome is a number in which the digits would read the same forward and backward.

### 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?

### 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?

### Rhonda's Zip Code

Rhonda’s zip code has five digits. Two of the digits are the same. One of the digits is three times another digit. Three of the digits are consecutive integers. The zip code starts with a zero. What is the largest possible sum for the digits of Rhonda’s zip code?

### 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?