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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Note: a palindrome is a number in which the digits would read the same forward and backward.
How many two-digit numbers are there such that the digits match at least one of the following patterns:
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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?
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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 They have been replaced by x and y. Find the values of x and y.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
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