My Math Forum > Math 4 congruent equil. triangles with 6 matches in 2-D (my puzzle)

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 April 4th, 2016, 07:41 AM #1 Banned Camp   Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191 4 congruent equil. triangles with 6 matches in 2-D (my puzzle) . How would you make exactly four congruent equilateral triangles with just six matches of equal length in two dimensions? No other triangles may be created when you are done. Matches may not be bent, torn, or separated into other matches. Match ends do not necessarily have to join other match ends. Specifically speaking, certain match ends might be free-standing. Matches may rest across/intersect other matches. - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - (You may find it helpful to work with drawing line segments to represent matches.) Thanks from manus
 April 4th, 2016, 05:06 PM #2 Global Moderator   Joined: May 2007 Posts: 6,759 Thanks: 696 Star of David. Six triangles surrounding a hexagon. Thanks from manus
 April 4th, 2016, 05:29 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025 Methinks not allowed, because 2 other equilateral triangles (sides = matches) are formed. Same thing with a square: works ok, but extra right triangles created. MMBt s'got a dilly there! Thanks from Country Boy, manus and Joppy
 April 5th, 2016, 02:12 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,634 Thanks: 2080 Here's a rough sketch: Matches.PNG Thanks from manus
 April 5th, 2016, 02:41 AM #5 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,155 Thanks: 731 Math Focus: Physics, mathematical modelling, numerical and computational solutions It is dangerous to go alone. Take this *hands over 6 matches* Thanks from manus
 April 5th, 2016, 06:44 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025 Skip, methinks your diagram is showing 5 triangles; includes a larger one side=match. Benit: you been drinking? Thanks from Benit13 and manus
 April 5th, 2016, 09:49 AM #7 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025 Found the darn thing (one shown on left): https://www.google.ca/?gws_rd=ssl#q=...ith+6+matches+ Thanks from skipjack and manus
 April 5th, 2016, 04:11 PM #8 Global Moderator   Joined: Dec 2006 Posts: 20,634 Thanks: 2080 Thanks, Denis. There is one rather nice, rotationally symmetrical solution (the one with a central triangle surrounded by three more triangles) at that site. I see that skeeter has posted below a version of it that reduces the number of "free" match ends (three such ends is probably the minimum possible). I like mathman's Star of David idea. It produces six congruent triangles in an elegant, symmetrical configuration, but one can modify it slightly to remove two of those triangles. In the diagram below, I've done that, and extended the matches slightly so that all the ends of the matches are "free". This makes my diagram very similar to one of the answers at the page that Denis linked to. Star.png Obviously, the horizontal match at the upper right of the above diagram can be moved to various other positions to create (after slight movements of other matches) various other solutions, including the solution I mentioned in my opening paragraph above. All of the correct solutions at the site that Denis found can similarly be obtained from the Star of David configuration. Thanks from manus Last edited by skipjack; April 5th, 2016 at 04:36 PM.
April 5th, 2016, 04:21 PM   #9
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Joined: Jul 2011
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 April 5th, 2016, 05:02 PM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,415 Thanks: 1025 Hey, real cute Skeeter...the Star of Texas ? Quick...go get a copyright on it...before MMBt steals it Thanks from manus and Joppy

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