The Middle Palindrome
Pro Problems > Math > Number and Quantity > Number Theory > DigitsThe 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.
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.
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?
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?
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 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?
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 They have been replaced by x and y. Find the values of x and y.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
Sum of Digits
Find the sum of all the integers between one and 100 which have 14 as the sum of their digits.
Reverse Me
I'm a three digit number. Reverse my digits and subtract, and the result is 198. Reverse my digits and add, and the result is 1272.
What number am I?
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?
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.
Blogs on This Site
