Set of Five Digit NumbersPro Problems > Math > Number and Quantity > Number Theory > Digits
Set of Five Digit Numbers
S is the set of five-digit numbers such that the digits are in ascending order, there are no repeated digits, the sum of the first two digits is equal to the third digit, and the sum of the third and fourth digits is equal to the two more than the fifth digit. How many elements are in the set S? (Note that the leading digit cannot be a zero).
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Find the sum of all the integers between one and 100 which have 14 as the sum of their digits.
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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?
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If each jar of grape juice requires 20 grapes, how many full jars of grape juice can I make this year?
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 They have been replaced by x and y. Find the values of x and y.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
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.
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- The digits are perfect squares.
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- 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?
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