Mathemagical Box--A Mind Experiment

[Turtle]

___The way I think I can count the total possible prints is to construct a tree graph & simply count directly. I have only printed 20 different prints & I still don't know for sure how many more are possible.

 

___After making a few prints though, I realized each print actually counts as two, because you get the same result printing the order of 'sides' backwards. Also, I found something unexpected & that is some prints terminate after five 'sides'; this is because the last unprinted side does not end up adjacent to the 5th printed.

___I hope this clarifies this inky issue enough to prompt some solutions from you. I also have another use for the box I have not revealed. The magic continues.:hyper:

[Tormod]

Is the number of prints important to understand this thing?

[Turtle]

(Grinning ear to ear) No, not really. If you see that one of the uses is making prints, that's enough. The math is as you know my constant obsession. I give you this hint Tormod; the next 'mystery' use is musical. Any guesses?:cup:

 

This box is extremely in the vein of multifunctionality I brought up in the Lounge.:hyper:

[Queso]

w00t. musical. this should be fun.

[Turtle]

___No music yet; I don't know how to post more than a few seconds long music file. I also wandered off & entangled myself in some other threads. No matter, the box is patient. Any music posting suggestions? :confused:

[Queso]

Upload it to an ftp server. if you don't have one, feel free to e-mail it to me and i'll upload it for you. i'll send you the link afterwards.

 

[email protected]

[Turtle]

I made a short recording of the box in use musically. Orb is going to try & post it up soon. :confused:

[Queso]

His recording can be found here:

http://www.mediapimp.net/jason/strumbox.mp3

that is exactly what i would do with it, too.

[Turtle]

Thanks Orb! I found a sheet where I was trying to work out the print count so next time I make scans I'll put it up. On first blush looking at it, I have about 3 different solutions penciled in & none right. Off the cuff, I think there are 72 different prints possible. Of these I have only printed 20.

[Turtle]

___Nothing really new to this I suppose, but I have noticed unused threads are closed & then I can't remove the attachments. Not that I want to remove the box photos, because actually it is the number of folks that have downloaded them that prompted me to refresh the thread.

___Feel free to comment or just look at the box, & of course if any of you math afficienados wish to correct my print count solution (72 different prints I believe I said last) please do.

___Enjoy. ;)

[Turtle]

___Talk about magical gibberish!@23??@42!1#$!. I have the prints pinned to the wall (I only fit 19 of the 20), & I have the digital photos in the camera; I don't have a clue as to the proper incantation for transferring said photos to this !$@#5423/// machine!! Persist I will. :hyper:

[Queso]

interesting. i think you and me share the same interest in having a lot of free time.

[Turtle]

___photo of prints I made from the box. Can you spot the ones that only use 5 sides as I described in post #18?

 

:rolleyes:

[Turtle]

In perusing my attachments in my User CP I see that 41 folks have downloaded the photo of the box attached in post #1 of this thread. The box is currently sitting in a black cloth bag with a red drawstring & accompanied by two other red & black magical devices. :rolleyes:

[Turtle]

___Draw or describe the other 2 red & black magical items in the bag with the box correctly & earn yourself some rep from Turtle. Mind you may have to wait a bit as I started giving rep to all who posted in Tormod's Birthday Wish thread & now it says I have to wait before giving more rep.

____The Majik is all around you. :QuestionM

 

 

 

:eek2:

[Turtle]

Well I'm still in limbo as to how many different prints I can make, but I saw another box problem here at Hypography with a bug crawling inside that Pyrotex solved nicely with showing the room unfolded. Any chance Pyrotex (et al) of confirming or falsifying my tentative answer of 72 different prints?

Thanks anyway.:) :)

[Turtle]

___If you ink up all 6 sides of the box & on a large sheet of paper place the box on any side you choose. Now without moving the box completely from the papaer, roll it to an adjacent side. Now roll it again to a different adjacent side & so on until you have a continuous print of the box. I have to wait for my friend to take a picture of one of the prints.

___Now the question is, how many different such prints can you (I) make? I have a method to solve this in mind, but I never actually did. I don't know the answer. So, if you can tell me a method & answer I suspect is right, I'll try to check it.

 

The question of how many different prints is not yet resolved.:confused: