Three Digit Number
Pro Problems > Math > Number and Quantity > Number Theory > DigitsThree Digit Number
I'm thinking of a three-digit number. The sum of its digits is between 15 and 20 exclusive. The product of my first and last digits is 18. I don't have any repeated digits, and my digits are not in either ascending order or descending order. I am a multiple of three, but not of six. What number am I?
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.
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?
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?
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?
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?
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 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?
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?
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?
Blogs on This Site
