My Three DigitsPro Problems > Math > Number and Quantity > Number Theory > Digits
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?
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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.
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?
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?
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?
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?
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?
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 They have been replaced by x and y. Find the values of x and y.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
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?
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?
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?