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Mystery Numbers (Posted on 2003-03-29) Difficulty: 4 of 5
I have chosen 3 different whole numbers less than 10, and have found several simple combinations that lead to perfect squares. Calling the numbers x,y, and z, the following combinations all yield a perfect square as the answer. (A perfect square is a number that has a whole number square root).

(x^2)y + (y^2)z + (z^2)x

x+y+z

z-y-x

xyz

(x^2)(z-1)

There are also several more complicated arrangements that lead to perfect squares, such as

x((z^2)-1)+z((y^2)-3)-x(yz-xy)

2xz+x+z

x((z^2)+x)+z(y^2)-(x^2)(z-y)

Given that these perfect squares are all different, and range between 0 and 100 (inclusive), can you determine x,y, and z?

See The Solution Submitted by Cory Taylor    
Rating: 3.4000 (5 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-11-23 04:04:14
negativesJack Squat2004-01-13 14:21:26
re(2): Zero?Cory Taylor2003-03-31 17:18:41
re: Zero?Fernando2003-03-31 16:09:41
QuestionZero?Bryan2003-03-31 05:49:08
re: SolutionFernando2003-03-29 20:53:49
SolutionRajat2003-03-29 08:01:09
Solution part 2Fernando2003-03-29 05:52:27
SolutionSolution part 1Fernando2003-03-29 05:49:56
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