Shannon V. OKeets > RE: Math Poser (1/16/2007 2:06:46 AM)

quote:
ORIGINAL: JAMiAM The problem is poorly posed... Define "manipulate" with regard to a symbol. Define "move". Are mathematical operations allowed to be implied? My own submission is as follows: Allow each of the individual numbers to be mapped as both the x,y coordinates in Quadrant I of the standard (Cartesian) plane. That is, 2 is implied to equal the point (2,2). The number 1 is implied to equal the point (1,1), 9 equals point (9,9), and 8 equals point (8,8). Finally, define a two digit sequence "ab" to be the drawing of the line segment between the two points a and b. Thus, 21 is the line segment containing points (2,2) and (1,1), while 98 is the line segment containing the points (9,9) and (8,8). Then, when we compare the lines defined by the two above described line segments, we see that they are indeed, both the same. There...no symbols "moved" and only "manipulated" in the sense of being used within defining statements, and mathematical operations. The problem is intentionally loosely stated, to allow the imagination to roam. Your solution could be reduced to a single dimension, with the distance from 1 to 2 being the same as the distance from 8 to 9. I like the visual aspects of your solution, but it does have that assumption about an underlying grid. This is not the third conceptual solution I have. Actually, no one has even given the second solution so far.



