Coffee MathPro Problems > Math > Number and Quantity > Number Theory > Digits
Johann was writing out a math problem when he spilled some coffee on his paper. The result was that some digits were covered up, as shown below.
♦7♦ + ♦♦9 ----- 50♦
If all but one of the hidden areas have the same digit, find all possible values for the sum of the hidden digits
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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.
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_ _ _ x _ _ x _ =
What is the largest possible value you can create?
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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 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?
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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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