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