[Guest]

in the classic tower of hanoi puzzle, you are given 5-7 disks on top of each-other, with each disk increasing in size from top to bottom. there is a rod standing vertically going through the center of the disks, and two more vertical rods that are empty. your goal is to move one disk at a time such that no bigger disk is placed on a smaller disk, and all 5-7 disks end up stacked again on a new rod.

well now for the twist. there are now 3 empty vertical rods and a new restriction. that restriction is that you can only place a smaller disk on top a particular larger disk, or a larger disk onto a smaller one, once. for example, if you put the first disk directly on top of the fourth disk, you cannot do so again.

try to solve it with 5 disks, then 6 disks, then 7 disks.

can this new puzzle be solved? if so, what's the solution?

[superprismatic]

in the classic tower of hanoi puzzle, you are given 5-7 disks on top of each-other, with each disk increasing in size from top to bottom. there is a rod standing vertically going through the center of the disks, and two more vertical rods that are empty. your goal is to move one disk at a time such that no bigger disk is placed on a smaller disk, and all 5-7 disks end up stacked again on a new rod.

well now for the twist. there are now 3 empty vertical rods and a new restriction. that restriction is that you can only place a smaller disk on top a particular larger disk, or a larger disk onto a smaller one, once. for example, if you put the first disk directly on top of the fourth disk, you cannot do so again.

try to solve it with 5 disks, then 6 disks, then 7 disks.

can this new puzzle be solved? if so, what's the solution?

Quite easy. It only requires 1 empty rod. Just move each disk, in order, from the first rod to the second one. Then go back. Each disk was placed on top of a particular other one just once.

Quite easy. It only requires 1 empty rod. Just move each disk, in order, from the first rod to the second one. Then go back taking each disk from the second rod to the first. Each disk was placed on top of a particular other one just once. Or perhaps I am missing something?

What's wrong with the spoiler? I get my last 2 posts after each other. The second spoiler is what I mean to say.

[Guest]

re-read the first paragraph.

in particular, they end up on a new rod.

you can use the original rod for temporary storage though.

[Guest]

if you have a tower of disks stacked like a pyramid with the smallest on top and largest on bottom...call each disk, disk 1-5(1 being the smallest)...and you have 3 empty rods to utilize...

move disk 1 to an empty rod..disk 2 to a different empty rod...now move disk 1 on top of disk 2..move disk 3 on top of disk 1...move disk 4 to an empty rod...move disk 5 on top of disk 3..move disk 4 on top of disk 5..from bottom to top it goes: disk-2,1,3,5,4...does that work?

Edited July 24, 2009 by James8421

[Guest]

There is no need for thre empty rods... You transfer all disks from rod num. 1 to rod num. 3, one by one. Now you should have a piramid upside down. Now transfer disks from rod num. 2 to num 3, one by one. I must be missing something in your instructions... I don't see a problem in this (new) puzzle?

[Guest]

that a disc can not be placed again on another disc

[Guest]

that a disc can not be placed again on another disc

Why did you use two rods??? can't you just move all discs to rod num. 2???

|1| | | | |

|2| | | | |

|3| | | | |

|4| | | | |

|5| | | | |

|6| | | | |

|7| | | | |

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

| | |7 | | |

| | |6 | | |

| | |5 | | |

| | |4 | | |

| | |3 | | |

| | |2 | | |

| | |1 | | |

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

| | | | |1|

| | | | |2|

| | | | |3|

| | | | |4|

| | | | |5|

| | | | |6|

| | | | |7|

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

The limitation is, that you can put each disk on any other only once. That was my understanding...

Is the limitation that you can not put more than one disc on the same rod/bottom disc in consecutive steps?

[Guest]

restriction is that you can only place a smaller disk on top a particular larger disk, or a larger disk onto a smaller one, once. for example, if you put the first disk directly on top of the fourth disk, you cannot do so again.

Well, I understood that if you have a disc X placed above or below a disc Y, they can not be put next to each other again while makiing the transfers.

[Guest]

ok...

Here's a question / something to think about:

What is the maximum number of discs that can be used in tower of hanoi puzzle so it can still be solved?

there is no limit in the number of discs

[Guest]

ok...

Here's a question / something to think about:

What is the maximum number of discs that can be used in tower of hanoi puzzle so it can still be solved?

there is no limit in the number of discs

The original Tower of Hanoi puzzle or with this modified version...

On second thought, in both cases, the answer would be no limit

[Guest]

yeah deegee has it, fairly simple really, but if limit it to three rods not sure its possible to solve.

[Guest]

Until today I didn't think about the towers since I was a kid... with this modified puzzle it got me thinking about "the original"... at first it seems as "the original" has a limit for the number of discs but in fact there is no limit, only the number of permutations gets ridiculously high with each added disc... And when you think about this, it's quite a trivial question, but at first glance...

Anyway, I found it amusing and I thought I would share it...

[Guest]

Isn't the whole point of the Tower of Hanoi puzzle the fact that you can never put a larger disc on top of a smaller disc? At least thats how I understood it. I don't see the puzzle behind it otherwise.