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Find the Number
My digits are all odd, and they add to 18. My first digit is four more than my last digit, the product of my digits is between 300 and 315, and I am less than 100,000. If my digits are not in descending order, what numbers could I be?
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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).
I am a three digit number, and the following things are true about me:
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- My first digit is four times my second digit.
What number am I?
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_ _ _ x _ _ x _ =
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♦7♦ + ♦♦9 ----- 50♦
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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 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?