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JEK595
Just a Wandering Enigma

 Posted: Thu Feb 21, 2002 6:51 pm    Post subject: 1 A few dissection puzzles: 1. Dissect three identical squares like so: Divide one into three unequal parts, divide on into two unequal parts, and leave one whole. Then arrange those parts to form one larger, perfect square. 2. Dissect a Greek cross into nine pieces that can fit together to form either five small squares or one large one. 3. Divide a perfect pentagonal star into twelve pieces which can be rearranged to form four smaller, perfect pentagonal stars. 4. Divide a perfect pentagonal star into eighteen pieces which can be rearranged to form five smaller, perfect pentagonal stars. 5. Divide a perfect square into five pieces which can be rearranged into either a trapezoid with two right angles, a right triangle, a perfect Greek cross, or a parallelogram. 6. Divide a perfect nonagon into fifteen pieces which can be rearranged into three smaller, perfect nonagons. ------------------ -grace the mind with puzzles, games, and tapioca.- -If at first you don't succeed, try, try again. (Not suitable for skydivers.)
JEK595
Just a Wandering Enigma

 Posted: Fri Feb 22, 2002 4:18 am    Post subject: 2 bump C'mon. Try 'em.
groza528
No Place Like Home

 Posted: Fri Feb 22, 2002 8:45 am    Post subject: 3 what's the definition of a 'Greek Cross?'
impossibleroot
Hi-Keeba!

 Posted: Fri Feb 22, 2002 4:36 pm    Post subject: 4 Believe me, I *am* trying the first one and it's killing me! I am learning a lot about dissections in general though, esp. that hinged dissection (triangle into square) -- very cool. Don't tell me how, but is there a general way to solve these or do you just have to mess with it till you've got it?
ralphmerridew
Daedalian Member

 Posted: Fri Feb 22, 2002 8:43 pm    Post subject: 5 A greek cross: code:``` +--+ | | +--+ +--+ | | +--+ +--+ | | +--+ ``` Or, a square, plus a congruent square attached to each side.
Jen Aside
Daedalian Member

 Posted: Sat Feb 23, 2002 1:19 am    Post subject: 6 1. sounds like a tangram, but I'd have to remember what the composition is to tell for sure.
groza528
No Place Like Home

 Posted: Sat Feb 23, 2002 9:43 am    Post subject: 7 2. I'm pretty sure this works. First the easy part: dissect the cross into 5 identical squares (one at each 'arm' and one in the center.) Then dissect four of these squares in the following way: the cut goes from one corner to the midpoint of a non-adjacent side. The five identical squares are obvious, to get the large square I'll try to put it in code. code:``` ---------------- |. . ....| | . .... | | . .... . | |.... . | | . ....| | . .... . | | .... . | |.... . .| ---------------- ``` Hope that's understandable
Milt
Daedalian Member

 Posted: Mon Feb 25, 2002 2:17 am    Post subject: 8 I tried number 1. Any hope of a clue?
Coyote

 Posted: Mon Feb 25, 2002 10:32 am    Post subject: 9 Set the three squares side by side to make a 1x3 rectangle (ABCD) Mark point E 1.7321... units from A (SQRT 3) Mark point F SQRT 3 from D Cut from C to E, making triangle ACE Cut from F to G (which lies on line CE), making triangle CFG Slide triangle ACE along line CE until C meets G Move triangle CFG up so that CF lies on EB code:``` E A ----------------------------+--------------------- B | | | | | | + | | | | G | | | | | | | | | | | | | | | | | | | | | | C ---------------------+----------------------------- D F ``` Hope that made sense.
Milt
Daedalian Member

 Posted: Mon Feb 25, 2002 2:41 pm    Post subject: 10 Thanks Coyote! [This message has been edited by Milt (edited 03-04-2002 12:47 PM).]
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