Discuss Overhanging stacks puzzle here

[Dragon Phoenix]

Go ahead


[This message has been edited by Dragon Phoenix (edited 09-19-2002 01:59 AM).]

[Skellum]

Overhanging Stacks

I assume you are allowed to use only one top and one bottom token?

Using precise scientific instruments (some drafts pieces) I can get: An offset of almost one whole reindeer bone token diameter. Maybe the sweat from my fingers helped them stick?

[margitsw]

With an infinite amount of tokens the answer is infinity!

[margitsw]

This is almost a chestnut.(I think)
As I said, given infinite tokens, answer is infinite
However, given that he brought back the tokens then it must be
a finite number.
If tokens <= 5, Offset < 1
If tokens > 5, Offset > 1
And I've found the formula.

[margitsw]

How do you get in contact with the puzzle poser ?
Or Do you wait till he/she answers here ?

[This message has been edited by margitsw (edited 09-19-2002 02:16 PM).]

[EricSolomon]

Yes, the overhang puzzle is a 'chestnut'. The centre of gravity of the body formed by all discs from the top down to disc 'n' must lie over disc 'n', for all 'n'.

Eric Solomon

[Sofis]

quote:

---

How do you get in contact with the puzzle poser ?
Or Do you wait till he/she answers here ?

---

Email is probably fastest. Asking questions here works too, but I don't tend to check this forum very often, so that might take longer.

BTW, in regards to this puzzle being a bit of a chestnut: I did indeed not come up with it myself. It was posted in VSP in May 2000, and I rewrote it into publishable form and wrote a solution.

[Saffronhil]

Bone tokens: bottom token laid flat, all other tokens are on edge through the top:}

[Lucky Wizard]

Saffronhil, regardless of what the solution is, the solution will be much easier to attain if you keep them all horizontal.

And Skellum's answer sounds right to me.

[margitsw]

[i_h8_evil_stuff]

*sigh* everyone's doing this a hard way.

using only 2 bone discs, the answer is infinite.

code:

---

                                       ------


                                       | Bone |


                                        ------


                                     ------------


 ------                             | Box, step, |


| Bone |                            |  or other  |


 ------    <--Infinite distance-->  |   object   |

---

Note: the second one is stacked(on top of the box).


------------------
The name explains it all.

[This message has been edited by i_h8_evil_stuff (edited 09-21-2002 08:08 AM).]

[CrystyB]

keep tokens only @ integer and integer/2, with the stacks growing in height as to top token goes rightwards:

code:

---

          /---\


          |   |


        /-+-+-/


        |   |


      /-+-+-/


      | 4 |


    /-+-+-/


    |12 |


  /-+-+-/


  |36 |


/-+-+-/


|108|


\---/

---

Keeping twice the number of tokens that are offset in the base stack ensures the C-of-G remains at 3/4th of the sustaining base. For every stack (except the topmost), so that the whole thingie is recursive, and you can go any length. But not infinity. (reply 26 makes for a nice reading )

[This message has been edited by CrystyB (edited 09-21-2002 11:41 AM).]

[margitsw]

LOL Crysty
How did your test go ?

[CrystyB]

tnx, the first one was easier than i expected. I got a 9- (i think it's like a B+). The second one (on monday) will be a killer though.

[apps]

disks- offset approaches as a limit 1/2 the radius of the largest disk-
assume the disks are stacked largest on bottom to smallest on top-
define offset to be distance from the right edge of the bottom disk to right edge of top disk

[mathgrant]

We can use glue too.

------------------
GL DPWestley: I had my backspace key removed and a beverage dispenser pur in it's place. See? I can't go back and fix "put."
GLmathgrant: I once was banned from a M:TG tourney for bringing over 50 banned cards! They were Ace of Clubs, Ace of Diamonds, Ace of Hearts, Ace of Spades, 2 of Clubs. . .

[Alana]

It's easy as pie. They are all lying down flat on an angle as you look straight down should you change the angle that you are looking they are straight so don't. and if you are at the same height as them look across and they are as far as they can be touching

[Jim]

Methinks the answer is approximately (n-2)*d where n is the total number of tokens and d is the diameter of each.

Each new token overlaps the previous by an infinitely small amount which creates a "stack" even though each one is touching the desk at one edge. I saw no requirement that the stack be balanced such that onny the bottom token touches the desk.

[margitsw]

Well with square or rectangular objects the overhang can be calculated as
(1 + 1/2 + 1/3 + 1/4 ... 1/n) / 2
which inreases (slowly) to infinity.
I think that this might apply to circular objects.
Crysty ? Math ?

[antodoyle]

The Queen of VSP is correct. The question must be general, because we don't know anything about the weight distribution in the tokens. So therefore the answer must be an infinite distance, with infinite tokens, spiralling up and out from the token at the bottom of the pile.

[XGUY]

Look at a penny it is not perfect it is tapered to one side the simple fact is you cant stack the bones up b/c they are tapered and the angle is approprate to how high you stack them if you turn one exactly 180 degrees opposite to the one below it you could stack them infinately but otherwise it depends on how you stack them as you progress

[TA]

By following the basic pattern shown below, the lateral distance between the top and bottom disk can approach infinity -- assuming the disks don't break.


====
==== ====
==== ==== ====
==== ====
====
This however requires quite a bit manual dexterity and/or super glue. -T-

[margitsw]

Here's a demo with blocks.

[margitsw]

Wow and another one for for the QSP !