2008 Solving the WASL Questions of Doom
posted by November 6 at 18:58 PMon
Winding down—still at work—from my day, I decided to solve the WASL questions of doom.
The easiest was the Tom, Dick and Harry one.
Harry, earning more than the manager, cannot be the manager, nor the teller (that earns the least.) Therefore Harry is the Cashier.
Tom cannot be the teller, as he has a sister. Since Harry is the Cashier, that makes Tom the manager.
Dick is the teller by default. Sucks to be him, being poorest paid.
Total Time: 2 minutes, using a neato match-chart.
65 sides, by my calculation.
5 on each short side x two short sides = 10
25 on each long side x two long sides = 50
5 on the top x 1 top = 5
Total = 65
I did this by making a little engineering plan style drawing.
Total time: 2 min.
This fucking compactor/cube problem was the worst.
x is the edge size of the older compactor, and y is the edge size of the newer compactor.
We’re told x > y and x and y are integers.
The volume of each cube is x^3 and y^3.
Each cube has twelve edges, so the total length of all the edges on both cubes is 12x + 12y.
Some asshole observed the following:
x3 + y3 = 12x + 12y
I spent much misery in algebra, attempting to get this down to something edible. My misery was unconstrained.
Among many others, I can make it all of the following:
x(x2 -12) + y(y2 -12) = 0
x3 / (x+y) + y3 / (x+y) = 12
and my personal favorite manipulation:
x4 + y4 + x^3y + xy3 -12 = 0
at this point, I became stuck, and brute forced it. (I have a feeling the last equation above is readily solvable. I got fed up, and realized that there aren’t that many integral candidates that even potentially would work.)
x = 4, y = 2 satisfies the initial equation.
4^3 + 2^3 = 12(4+2)
64 + 8 = 72 = 12*6
Total time? 30 fucking minutes.
Who the fuck “notices… that the combined volumes of one cube from each compactor was numerically the same as the combined length of all their edges.” I work in a lab, a real scientific lab, and can guarantee such a situation never happens. Nor will it ever happen. I mean, really, this has no business being a word problem. Fucking stupid. I’m glad she lost.