CTK Insights

Archive for the 'Algorithms' Category

28 May

Biochemical Algorithms and School Algebra

You know, the nurses there did not appear to lack in intelligence. They carried out intellectually demanding jobs, most of the time sitting in front of networked computers or handling mobile devices. I did not dare to asked her whether or not she took an algebra course either in high school or a college. It was obvious that, even if she did, the powerful algebraic tools that were (and are) being peddled to students for their own good by the education establishment had little effect on her thinking or the excellent manner in which she carried out her duties.

26 Apr

Not too easy - not too difficult

TweetThe other day, while driving my HS senior son to school (he could have taken a bus, but, for one, his time is at a premium; also, the drive gives us an opportunity for a small chat), we talked about how words with different basic meanings may mean the same thing in certain contexts. As […]

13 Apr

7 or 22

Without ever trying to answer such questions, I was always confident that the poster (if not the author) were smugly awaiting a definite reply, although, even with the most benevolent interpretation, the problem has to be considered ill-posed, like that of asserting the next term in a given sequence

01 Aug

Distance to the Horizon on the Fourth of July

TweetI had the luck to celebrate the past 4th of July with our friends in their newly acquired home just above the marina in Atlantic Highlands, NJ. The view from their backyard was absolutely breathtaking. The ambient light that appeared to blur the background made the view even more enchanting. Here is a map that […]

17 Oct

Elementary Problems that Beg for Generalization

TweetIn a well known puzzle, a father willed to his three sons camels, with the proviso that of the inheritance should go to the oldest among them, with being due to the middle one and to the youngest. Shortly after the father's death, a wise man riding on his camel through the village noticed the […]

20 Mar

The Golden Ticket: P, NP, and the Search for the Impossible

The only known serious approach to the N versus NP problem today is due to Ketan Mulmuley from t he University of Chicago. He has shown that solving some difficult problems in a mathematical field called algebraic geometry (considerably more complex than high school algebra and geometry) may lead to a proof that N ≠ NP. But resolving these algebraic geometry problems may require mathematical techniques far beyond what we have available today.

19 Sep

A Magical Incident due to the Paypal's Policy

I believe that the discrete variant makes the solution more transparent. For example, think of coffee and cream not as liquids but as collections of molecules. Since the number of molecules in the two glasses remains the same even after repeated iterations, cream molecules in the "water" glass come at the expenses of the water molecules in the "cream" glass and, therefore, the two quantities are equal.

02 Aug

Evolution of a problem and an answer

TweetIn grades 1 through 5, my little boy went to a private Hebrew school. Every day I drove him there and then picked him up at the end of the day - half an hour drive each way. We spent the combined hour mostly talking of mathematics. For the next three years he took the […]

07 Jun

A Kindergarten Activity As a Problem for Adolescents

TweetTwelve kids stand in a circle, a kid per one of twelve marked spots. Every now and then one moves clockwise, another counterclockwise to an adjacent position (which may be occupied by more than one kid or be empty.) Is it possible that after a while all of them stand at the same spot? The […]

24 May

Three Checker Game on a One Row Board

TweetThe setup for the 2-players game described below consists of three checkers placed on a K×1 board: A move consists in picking one of the outside checkers and placing it anywhere between the other two. Here's a sequence of two successive moves. As usual, players take turns. The one who can't make a move loses […]

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