Rhonda's Zip Code
Pro Problems > Math > Number and Quantity > Number Theory > DigitsRhonda'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?
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
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.
Happy New Year
Happy New Year! I am a four-digit year, and my last two digits are a perfect square. The sum of my first and third digits is a perfect square. My second digit is a perfect square. All my digits add to a perfect square.
If you subtract my first, second, and third digit from my last digit, you get a perfect square.
If you subtract my third digit from my first digit, you get a perfect square.
Oh, by the way, I'm a perfect square.
What year am I?
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?
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?
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?
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?
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.
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.
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?
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?
Blogs on This Site
Like us on Facebook to get updates about new resources