Of late, I seem to be stuck in a loop with books. I read parts of them and then seem to come back to the very beginning of the same book and discover something new. I am stuck in a partial loop in an "open form". Of late that has happened with Concrete Mathematics. I started with the first chapter on Recurrent problems - you seen the irony :)
Anyway, one of the problems is Towers of Hanoi with limitation. Don't go to the intermediate peg directly, go to the destination peg and then go to the intermediate peg. I remember reading somewhere that Knuth used Macsyma for a bunch of verification on Metafont (I could be wrong). I decided to use Maxima. I used the solve_rec procedure
load(solve_rec);
The recurrence equation is
solve_rec(a[n] = 3*a[n-1] + 1, a[n]));
and Maxima was quick to respond with the answer
I wonder if Knuth is right, in the future most of the burden of mathematical complexity of finding a solution will be delegated to computers.
Anyway, one of the problems is Towers of Hanoi with limitation. Don't go to the intermediate peg directly, go to the destination peg and then go to the intermediate peg. I remember reading somewhere that Knuth used Macsyma for a bunch of verification on Metafont (I could be wrong). I decided to use Maxima. I used the solve_rec procedure
load(solve_rec);
The recurrence equation is
solve_rec(a[n] = 3*a[n-1] + 1, a[n]));
and Maxima was quick to respond with the answer
I wonder if Knuth is right, in the future most of the burden of mathematical complexity of finding a solution will be delegated to computers.
