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.
5 comments:
castor oil with price is a liquid that you take by mouth. It's typically taken during the day because it works quickly. The dose of castor oil used to treat constipation in adults is 15 milliliter.
copper bottle could improve your immune system, aid digestion, decrease wound healing times, and even boost your tan.
Today, it is deemed as one of the healthiest oils, loaded with essential nutrients. In Ayurveda, gingelly oilis valued for its medicinal properties. It is said to be good for the skin.
Castor Oil Is Rich in Healthy Monounsaturated Fats. But the predominant fatty acid in Cold Pressed Castor Oil is a monounsaturated fat called oleic acid, making up 73% of the total oil content.
All of the fats and cold pressed coconut oil that we eat are composed of molecules called fatty acids. Biochemically, fatty acids are composed of a chain of carbon atoms connected to one another by chemical bonds..
Vellam is molasses made from sugarcane.karupatti is jaggery got from the palmyra tree.
nattu sarkarai is the sweetner extracted from the cane, bamboo and cane is the same thing. They are both grasses in the Poaceae family of grass.
One of the most important things to keep in mind is - that cold pressed oil behaves differently when heated, it changes texture, color, taste as well as it's nutritional properties.
marachekku oil is very good for health & it is famous for cooking in India
When oil is refined, it loses a lot of nutrients but cold pressing it in a chekku oil ensures that you retain all of it,” says the 35-year-old who works in a software firm. you can try with this oil next time
Samai noodles is healthy and tasty. Suitable for all age groups.
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