(Count(n,n,n))! a universal solution. (Bob)

]]>By the way, by hand, I get:

b*y

= (20/z)*y (since b*z = 20)

= (20/17)*c*y (since c*z = 17)

= (20/17)*(2017/x)*y (since c*x = 2017)

= (2017/17)*a*y (since a*x = 20)

= 2017 (since a*y = 17).

Maple, by the way, does a more complete job of describing all possible solutions, and returns

{a = 17/y, b = 2017/y, c = 34289/(20*y), x = (20/17)*y, y = y, z = (20/2017)*y}

]]>I had an algebraic trick in mind to find the solution, though working with my sons last night, they were far more keen on trying to find values for a, b, c, x, y, and z and then using those values to determine b*y.

]]>One could solve this system by hand, but that seems rather tedious, and therefore can’t possibly be the intended method of attack.

]]>I am a long time reader, but I never comment. But I feel compelled to do so. I am almost 5 feet tall, my husband is 5’8″ tall. We have three sons. My oldest is 5’6″ on a good day. My middle son is 5’9″ tall. My youngest (who is 16 and still growing) is 6’0″.

Clearly, the solution is for you to have another child. 🙂

]]>THE BEAST!!!! ]]>