Three Jog Knight.The rock band Three Dog Night started to become popular in the late 60s. At that time, I created a puzzle “Puzzle solving” redirects here. For the concept in Thomas Kuhn's philosophy of science, see normal science. A puzzle is a problem or enigma that challenges ingenuity. to lead into a lesson in one of my math classes which I called the Three Jog Knight. Its purpose was to introduce some ideas about vectors; the puzzle was to show all of the ways in which a knight could be moved from the lower to the upper square in this chessboard in exactly three moves. One of the ways is shown in the figure. [Figure for 3 jog knight] The answer turns out to have a pleasant surprise. Several months ago while I was having trouble going to sleep, I thought about this puzzle and realized that it would be interesting to generalize generalize /gen·er·al·ize/ (-iz) 1. to spread throughout the body, as when local disease becomes systemic. 2. to form a general principle; to reason inductively. it by asking the following questions. The result for a one jog knight is obvious and the result for a two jog knight is fairly easy to imagine without making a drawing. [Figures for 1 and 2 jog knights] What about a four jog knight? Can you make a guess before drawing all of the possible paths? [Figure for 4 jog knight] I see from the internet that Three Dog Night is still making music! We have added a word component to Harold's Geometry geometry [Gr.,=earth measuring], branch of mathematics concerned with the properties of and relationships between points, lines, planes, and figures and with generalizations of these concepts. as exemplified in the word A for 1 Jog Knight and the word TOAD toad, name applied to certain members of the amphibian order Anura, which also includes the frog. Although there is no clear-cut distinction between toads and frogs, the name toad for the 2 Jog Knight. On the Answers" and Solutions page we give a word solution to the 3 Jog Knight using FLYING SAUCER flying saucer: see unidentified flying objects. . The 4 Jog Knight will require 32 letters. We leave this as a contest for the readers to enter. Perhaps to the 26 letters of the alphabet alphabet [Gr. alpha-beta, like Eng. ABC], system of writing, theoretically having a one-for-one relation between character (or letter) and phoneme (see phonetics). Few alphabets have achieved the ideal exactness. we could add another copy of the six vowels' to complete the 16 4-letter words required. A copy of Alphabet Dance will be awarded to the first successful solution. [ILLUSTRATIONS OMITTED] HAROLD JACOBS North Hollywood, California |
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