Games
Problems
Go Pro!

Fill in the blanks

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

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 They have been replaced by x and y. Find the values of x and y.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

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

Sum of Digits

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

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?

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?

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?

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

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.

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).

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.

 

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?

Reverse Me, The Middle Palindrome, Three Digit Difference, Rhonda's Zip Code, All My Digits, Three Digits, sum and product, Happy New Year, Three Digit Number, Four Digit Number, Find the Number, I Have Three Digits, Grapes on the Vine, Three Digit Number, My Three 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