All My Digits

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

Presentation mode

Problem by malimil

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

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 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.

Digits in a Multiplication Problem

You must use each of the integers from 0 to 5 exactly once to fill in the blanks in the multiplication problem below.

_ _ _ x _ _ x _ =

What is the largest possible value you can create?

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?

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?

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.

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?

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'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?

Sum of Digits

Find the sum of all the integers between one and 100 which have 14 as the sum of their digits.

Happy New Year, Three Digits, sum and product, Grapes on the Vine, Fill in the blanks, Rhonda's Zip Code, Set of Five Digit Numbers, Coffee Math, My Three Digits, Back to Back, Find the Number, Two Digit Pattern Matching, Fiona's Telephone Number, Palindrome Addition, Five Digit Number

Blogs on This Site

Book Scrounger

Reviews and book lists - books we love!

Ask Professor Puzzler

The site administrator fields questions from visitors.

Like us on Facebook to get updates about new resources