The Middle PalindromePro Problems > Math > Number and Quantity > Number Theory > Digits
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.
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I am a four digit number.
The sum of my digits is 20.
The product of my digits is 600.
The difference between my first two digits is 2, and the sum of my middle two digits is 11.
What number am I?
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?
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?
I am a three digit number, and the following things are true about me:
- The product of two of my digits is 8.
- The sum of my digits is 13.
- My first digit is four times my second digit.
What number am I?
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?
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?
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?
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?
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?
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?