Five Digit Number
Pro Problems > Math > Number and Quantity > Number Theory > DigitsFive 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?
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.
Similar Problems
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).
Sum of Digits
Find the sum of all the integers between one and 100 which have 14 as the sum of their digits.
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.
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?
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?
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?
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?
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.
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?
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
Blogs on This Site
Like us on Facebook to get updates about new resources