Greek Cross Dissections

[ParaLogic]

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)!

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.

You can make a cut and re-assemble the resulting pieces before making a subsequent cut.

Edited March 18, 2013 by ParaLogic

[ParaLogic]

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.

[bonanova]

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.

[TimeSpaceLightForce]

[bonanova]

I'll bite.
Why is it not as obvious as it looks? N S E W and center.

[TimeSpaceLightForce]

[TimeSpaceLightForce]

[BobbyGo]

[TimeSpaceLightForce]

[ParaLogic]

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.

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.

You will need to figure #6 first!

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 March 22, 2013 by ParaLogic

[ParaLogic]

You will need to figure #6 first!

I meant for #7 :

[TimeSpaceLightForce]

6 cuts no re-assembling