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

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?

Three Digits, sum and product

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?

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?

Reverse Me

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?

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?

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?

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?