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Find the unique four-digit integer n with these properties:

 The last digit (the units digit) of n is 9.

 The digits of n add up to 27.

 Two digits of n are the same.

 n is a perfect square.

SmartMathMan  Jan 26, 2018
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2+0 Answers

 #1
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63^2 = 3,969  Meets ALL the conditions.

Guest Jan 26, 2018
 #2
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If x^2 ends in 9 then the x must end in 3 or 7

If x^2 is four digits then x must be between 32 and 99

 

So the only possibilities for x are

33, 37, 43, 47, 53, 57, 63, 67, 73, 77, 83, 87, 93, 97

 

Square each of those and find the one/s that fit the other two requirements :)

Melody  Jan 26, 2018

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