Games
Problems
Go Pro!

Coffee Math

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

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

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

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?

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?

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 They have been replaced by x and y. Find the values of x and y.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

  1. The product of two of my digits is 8.
  2. The sum of my digits is 13.
  3. My first digit is four times my second digit.

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.
 

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 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?

 

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?

Sum of Digits

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

 

Digits in a Multiplication Problem, Five Digit Number, The Middle Palindrome, Set of Five Digit Numbers, Rhonda's Zip Code, Fiona's Telephone Number, All My Digits, Four Digit Number, Happy New Year, Three Digits, sum and product, Reverse Me, My Three Digits, Back to Back

Featured Games on This Site

Match color, font, and letter in this strategy game
Trap all the dots in this problem-solving puzzle

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