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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1764.0. ""Conservation" of faces" by AUSSIE::GARSON (nouveau pauvre) Mon Jun 14 1993 03:15

    This is from "The Ghost from the Grand Banks" by Arthur C. Clarke, who
    attributes it to a high-school intelligence test.
    
    
    Imagine two tetrahedrons and a pyramid all having edges with a common
    length. Each tetrahedron has four faces and the pyramid five.
    
    If the two tetrahedrons are placed together so that a pair of congruent
    faces coincide then the resulting object has a total of six faces. This
    is not suprising since two of the faces "disappear".
    
    Q: If one of the tetrahedrons and the pyramid are placed together in
    the same way, how many faces does the resulting object have?
    
    Answer after the form feed.

    Not seven which one might logically guess, but in fact five. I couldn't
    visualise this. After some work with scissors and cardboard it appears
    that the resulting object is a sheared (triangular) prism. The tetrahedron
    just sort of merges into the pyramid without adding any faces at all.
    Mind boggling!

T.R	Title	User	Personal Name	Date	Lines
1764.1	pyramid of chops	HERON::BUCHANAN	The was not found.	`Mon Jun 14 1993 11:52`	13
	Take a (big) tetrahedron, and chop it in two, parallel to two opposite edges of the tetrahedron. The cross-section is a square. The two pieces that you now have are congruent. From each piece, chop off the two regular tetrahedral corners (edge length half that of the original tetrahedron). Then what remains of each piece is a square pyramid. So T+P+T + T+P+T = a tetrahedron. Alternatively, stick the two pyramids together, and see that you have a regular octahedron. Gluing tetrahedra to 4 non-adjacent faces returns you to the big tetrahedron. Andrew.
1764.2	SAT mistake?	RANGER::BRADLEY	Chuck Bradley	`Mon Jun 14 1993 20:20`	6
	this sounds vaguely familiar. i think the question was asked on an SAT test, back about 1978 or 1979. one of the students answered five and had it marked wrong, but complained and got his score changed. it was in the boston globe, so probably also in other papers.
1764.3	memories aint deceivin'	AUSSIE::GARSON	nouveau pauvre	`Mon Jun 14 1993 22:41`	6
	re .2 Clarke mentions that the printed answer was wrong and that one genius level student got the "right" answer. SAT = ?
1764.4		HANNAH::OSMAN	see HANNAH::IGLOO$:[OSMAN]ERIC.VT240	`Tue Jun 15 1993 16:08`	6
	We only got our SAT scores, we never got to see which questions we got wrong. How did that student get the details ? /Eric
1764.5	I don't know	RANGER::BRADLEY	Chuck Bradley	`Tue Jun 15 1993 16:34`	18
	> We only got our SAT scores, we never got to see which questions we got > wrong. How did that student get the details ? i don't know, and i'm not even sure of what i said in .2. i saw something in the paper, and i also recall hearing about it from Lynn Yarbrough. maybe he remembers more of the details. maybe the kid got a 790 and was confident enough that it should have been an 800 that he sued. it is now possible to get the answers, but for many years ETS was so closed they could have assigned the scores by a random number generator. maybe the incident happened after ETS was opened up, or maybe it was one of the incidents that forced it to open up, or maybe it was not the SAT at all. anybody want to do a literature search? NY Times index, Reader's Guide, some kind of education index. the details would be interesting, but not completely relevant to this conference.
1764.6		RUSURE::EDP	Always mount a scratch monkey.	`Tue Jun 15 1993 19:28`	6
	Re .4, .5: It happened after the answers became available. -- edp