Palindrome Addition

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

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.

Presentation mode

Problem by Mr. H

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.

Assign this problem

Click here to assign this problem to your students.

Similar Problems

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 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?

Find the Number

My digits are all odd, and they add to 18. My first digit is four more than my last digit, the product of my digits is between 300 and 315, and I am less than 100,000. If my digits are not in descending order, what numbers could I be?

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?

Happy New Year

Happy New Year! I am a four-digit year, and my last two digits are a perfect square. The sum of my first and third digits is a perfect square. My second digit is a perfect square. All my digits add to a perfect square.

If you subtract my first, second, and third digit from my last digit, you get a perfect square.

If you subtract my third digit from my first digit, you get a perfect square.

Oh, by the way, I'm a perfect square.

What year am I?