New problem idea - Hanoi towers
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Hello again! I decided to make a new topic so we can discuss the problem here.
As our father Rodion said Ah, right, I also thought about it several times (and perhaps someone... you? - already suggested it). The matter is I'm not sure how to make problem of it. E.g. We know there are three towers and there is strategy to do all transfers... Well, what should be the problem? That puzzles me a bit. Feel free to hint :) I suggest that new problem statement, INPUT, could be inspired by klotski. I pressume that you are familiar with this puzzle, if not here is some reading.
So my idea, is that we will be given number of towers, maximum capacity of towers
and we are to calculate the optimal solution i.e minimal number of steps to solve such a puzzle.
Ha-ha, Father Radovan :)
So my idea, is that we will be given number of towers
Do you mean three towers with some disks on each - or all disks are in a single pile but there are K towers and N disks at all (more than 3 or 4)?
Meanwhile I think one of the questions could be - given certain state of disks in 3 towers (i.e. as if at
some step in the middle of the game) - to calculate what is the next move (for optimal solution).
My initial idea was to modify the hanoi towers as we know it. For instance there would be more towers with more disks some towers could have certain capacity, so if there are 4 disks, we can place only 3 to certain tower for instance and the input data could be numbers representing disks and towers, let me use some pictures and my master MS paint skills combined with imgur. to show you what I mean, The problem task could be also similar to triangles task and we were to tell if the puzzle can be solved or no.
Do you mean three towers with some disks on each - or all disks are in a single pile but there are K towers and N disks at all (more than 3 or 4)? My answer is : or all disks are in a single pile but there are K towers and N disks at all (more than 3 or 4) but your first thought is also applicable or all at once perhaps too?
T - towers
D - disks
and simulation to tell optimal solution / or answer to "does this puzzle have solution"?
Or maybe appling both, optimal solution AND "does this puzzle have solution" for 2 new tasks as one would be the advanced version of problem.
I hope my explanation is understandable and idea being somewhat applicable.
I have become a bit puzzled by all this, but come up with two precise problems for Hanoi Towers with very large number of disks.
Let this be at issues #69 for now - I believe we can use one here and other at OpenAbbey.
It would be great also to create small JS game so we can embed it in problem statement page.
Sorry that I jumps in, but I want to also put in my 2 cents. I have a proposition of quiz: we are given randomly generated set of disks distributed on 3 needles. Needles are numbered starting from 0. Moves are encoded as follows: encodedmove = ( sourceneedlenumber ) * 3 + ( destinationneedle_number ).
Checksum is calculated in chain: checksum=(checksum * 11 + encoded_move) % 2000000011
2000000011 - this is arbitrarily chosen big enough prime number.
Disks on every needle are positioned in ascending order from top to bottom - smaller disk is always on the top of bigger one. All disk are of different size - no equal disks exist.
User is questioned for the checksum of the moves of the optimal solution placing all the disks on the number 2 needle .
There are quite a bunch of disks in setup (up to 100?, for example), so recursive approach is not suitable. Method of calculation of checksum allows to use linear programming approach. I have implemented solver for that quiz.
Rodion, how can I send you my code, if you are interested in? I can find your email.
Just popping topic up.
Alexandr, Hi!
That's correct :) Sorry, I sometimes got quite distracted by domestic matters etc, which is of course quite annoying for people... Hopefully I'll be able to put more attention to the matter in the upcoming period... There is "almost ready but yet unpublished" problem from Quandray, shame on me...