Happy New YearPro Problems > Math > Number and Quantity > Number Theory > Digits
Happy New Year
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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What number am I?
When Shrek asks Fiona for her telephone number, Fiona is a bit coy about it, and tells Shrek the following information:
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- There are no repeated digits in my telephone number.
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- The second three digits are in descending order.
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- The sum of the second three digits is 14.
What number should Shrek dial?
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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?
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_ _ _ x _ _ x _ =
What is the largest possible value you can create?
How many two-digit numbers are there such that the digits match at least one of the following patterns:
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- Neither of the digits are multiples of two.
- The digits add to 8.
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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?
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