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Greek Cross Dissections

Started by ParaLogic, Mar 18 2013 03:11 AM

Best Answer ParaLogic, 05 April 2013 - 02:53 AM

I think that's the best solution if you don't re-arrange any pieces until the end, but I didn't say you couldn't..?

 

I'll just share my solutions for #7 now, since this thread has passed on.

 

Spoiler for #7, no re-arranging (and no creativity)

 

Spoiler for #7, re-arranging (and creativity) allowed

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11 replies to this topic

#1 ParaLogic

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Posted 18 March 2013 - 03:11 AM

It's been a looong time since I last visited this forum. (I forgot the username/password for my old account.) But now I'm capable of making my own puzzles (I hope)!  :thumbsup:

Greek Cross 1.png

 

Find the minimum number of straight lines needed to cut a greek cross (example above) into pieces that can be re-assembled to make:

  1. One square
  2. Two congruent squares
  3. Three congruent squares (I don't actually know the answer--or if it's even feasible--but maybe you'll surprise me!)
  4. Four congruent squares
  5. Five congruent squares (It's not quite as obvious as it looks!)
  6. Four congruent greek crosses (I have a solution, but it's probably not optimal)
  7. Five congruent greek crosses (Same as #6)

I'm fairly confident that I have the optimal solutions for 1, 2, 4, and 5. I just threw in the others for an extra challenge. 

 

Spoiler for Note!


Edited by ParaLogic, 18 March 2013 - 03:13 AM.

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#2 bonanova

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Posted 18 March 2013 - 04:48 AM

Hi PL, it's nice to have you back!

If you remember your old username, we can probably fix it up for you to use again.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 TimeSpaceLightForce

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Posted 18 March 2013 - 01:08 PM

Spoiler for 1


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#4 bonanova

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Posted 19 March 2013 - 10:36 AM

Spoiler for 5


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 TimeSpaceLightForce

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Posted 19 March 2013 - 06:01 PM

Spoiler for 4


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#6 TimeSpaceLightForce

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Posted 19 March 2013 - 06:26 PM

Spoiler for 2


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#7 BobbyGo

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Posted 19 March 2013 - 09:13 PM

Spoiler for 5

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#8 TimeSpaceLightForce

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Posted 21 March 2013 - 03:02 PM

Spoiler for 2cuts


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#9 ParaLogic

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Posted 22 March 2013 - 02:31 AM

Sorry for the long wait with no reply; I've been very busy recently.

 

@TSLF: Your answer to #1 is correct, although there are really an infinite number of solutions (to any of these) with the same number of cuts. And your second answer to #2 is also right. (Much simpler than your first, no? ;))

 

BobbyGo has the best solution for #5.  :thumbsup:

 

I should also add a clarification: I have not seen any solutions that require you to flip or even rotate the pieces (yet). I realized that if you are allowed to rotate the pieces, you can cut down (heh) the number of moves by using this in conjunction with the Note provided in the OP. For now, let's avoid anything other than translations. 

 

That means that TSLF's answer to #4 is also good. I could do it with one fewer cut, but that would require some rotating.

 

After some consideration, I think I've found the best solutions for #6 and #7. There is an especially creative solution to #7 that I found while doodling on graph paper.  B))

Spoiler for Hint for #8

 

Unfortunately, I doubt that there is such a neat solution to #3. If it were to be done, I don't think any of the cuts would line up with the grid lines provided in my example picture.


Edited by ParaLogic, 22 March 2013 - 02:36 AM.

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#10 ParaLogic

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Posted 22 March 2013 - 02:42 AM

Spoiler for Hint for #8

I meant for #7 : :duh:


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