My Three Digits

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

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?

Presentation mode

Problem by Mr. Twitchell

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

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.

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?

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.

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?

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

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?

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.
The digits add to 8.
The digits are perfect squares.

Fill in the blanks

In the addition problem below, some digits are missing. They have been replaced by x and y. Find the values of x and y.

3xy2 + 3y1 = 40x3

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 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?

Fiona's Telephone Number, Set of Five Digit Numbers, Sum of Digits, Three Digit Number, Reverse Me, Rhonda's Zip Code, Four Digit Number, All My Digits, Three Digit Difference, Back to Back, Digits in a Multiplication Problem, Grapes on the Vine, Happy New Year, Three Digit Number

Understanding Coronavirus Spread

Exponential Growth and Coronavirus

A Question and Answer session with Professor Puzzler about the math behind infection spread.

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