Games
Problems
Go Pro!

Find the Number

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

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?

Presentation mode
Problem by BogusBoy

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

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?

Set of Five Digit Numbers

S is the set of five-digit numbers such that the digits are in ascending order, there are no repeated digits, the sum of the first two digits is equal to the third digit, and the sum of the third and fourth digits is equal to the two more than the fifth digit. How many elements are in the set S? (Note that the leading digit cannot be a zero).

Two Digit Pattern Matching

How many two-digit numbers are there such that the digits match at least one of the following patterns:

  1. The digits are both multiples of three.
  2. Neither of the digits are multiples of two.
  3. The digits add to 8.
  4. The digits are perfect squares.

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?

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 They have been replaced by x and y. Find the values of x and y.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

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.

 

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

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?

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?

Fiona's Telephone Number

When Shrek asks Fiona for her telephone number, Fiona is a bit coy about it, and tells Shrek the following information:

  • My telephone number has 10 digits.
  • There are no repeated digits in my telephone number.
  • The first three digits are in ascending order.
  • The second three digits are in descending order.
  • Both the last four digits and the last two digits are multiples of sixty.
  • My last four digits are not a multiple of 43.
  • My first three digits are the square of an integer less than twenty.
  • The sum of the second three digits is 14.

What number should Shrek dial?

Three Digit Number, Happy New Year, Grapes on the Vine, The Middle Palindrome, Three Digit Difference, Five Digit Number, Three Digit Number, I Have Three Digits, Digits in a Multiplication Problem, My Three Digits, Three Digits, sum and product, Back to Back, Four Digit Number, Sum of Digits

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy