Black Lab always has a welcome from me.
Like him, I am impressed by pinkman's extensive travels.
But this is about Curtis' ride. I hope I can attend, but February is a month full of unknowns for me. For instance, I need to get my chopper repaired ... no, not THAT kind of chopper! One of my teeth threatens imminent treachery, so I will be devoting a day to its rehabilitation.
pinkman, a friend proposed a puzzle based on 2011, and it is this:
Solve for x and y, to several decimal places:
x*x - y = 2011
x * y = 2011
Pretty soon, this turns into a cubic equation in x. I was amazed to learn that there is a formula, similar to the quadratic formula, for cubics, except it is a yard long and frequently has imaginary values that do or do not cancel out.
I wrote a brief Applesoft BASIC program that solved the problem to about six decimal places. But that was not enough, so I found a 1401 simulator, and I wrote an Autocoder program that solved for x to over 40 decimals. I plan to extend the accuracy about 100-fold when I am short of things to do. As it turns out, a 1401, IBM's wonder machine of the early 1960s, is great for such applications, because a "word" can be thousands of bytes long if you want it to.
Short of things to do, I said. That was the funny part.
P.S. I offered another 2011 riddle to my 1959 classmates, and indeed
one of them solved it. Find three positive integers a < b < c such that:
a*a + b*b + c*c = 2011
a*b + b*c + c*a = 1959