Mystery Numbers (Posted on 2003-03-29)

	Submitted by Cory Taylor
Rating: 3.5000 (6 votes)
Solution:	(Hide)
The expressions, when evaluated (in order) are 100,9,1,0,64,81,49,36. The values for x,y, and z are 4,0, and 5 respectively. The best starting point to determine the numbers lies in the following 2 equations; x+y+z -> because you know the square will be less than 25, and more than 5 (possibilities 16,9). z-y-x -> tells you that z >= (x+y). Also, the only possible squares are 4,1, or 0. Now consider that the first equation has a maximum value of 100. and you can conclude that the x+y+z equation is equal to 9, as any combination for 16 would cause the first equation to exceed 100, unless one of the numbers is zero, which would then force the other 2 numbers to be 7,9 - but these do not satisfy the z-y-x equation. Next, knowing that x+y+z is 9, you can conclude that z-y-x must be odd (the sum of the two equations is 2z, which must be even), leaving only 1 as a valid solution. Again using the sum of these two equations (2z), we get 2z=9+1, or z=5 Looking back at the first equation with the knowledge that z=5, and knowing that (x+y) must be 4, the only combination of (x,y) that leads to a square (100) is x=4 and y=0, completing the problem. There are of course, many other succesful methods for determining the variables' values.

	Subject	Author	Date
	answer	K Sengupta	2007-11-23 04:04:14
	negatives	Jack Squat	2004-01-13 14:21:26
	re(2): Zero?	Cory Taylor	2003-03-31 17:18:41
	re: Zero?	Fernando	2003-03-31 16:09:41
	Zero?	Bryan	2003-03-31 05:49:08
	re: Solution	Fernando	2003-03-29 20:53:49
	Solution	Rajat	2003-03-29 08:01:09
	Solution part 2	Fernando	2003-03-29 05:52:27
	Solution part 1	Fernando	2003-03-29 05:49:56