Towers of Dawnoi

[jere7my]

While washing dishes the other night, it occurred to me that I was unconsciously solving a modified Tower of Hanoi problem. I had three "posts": the two sink basins and the dish drainer. There were a bunch of plates randomly stacked on the first two, and my goal was to move all of them onto the third, large to small.

The rules:

• I can move multiple plates at a time between the two basin posts, but for stability reasons I can't place a stack containing a larger plate atop one containing a smaller one.
  
• I can only move one plate at a time onto the drainer post (since I can only wash one at a time).
  
• Once a plate goes onto the third post, it can't be moved again. (Practically speaking, this means I have to wash the largest plates first.)
  

Okay, it's not a particularly interesting or difficult problem, but I was amused at myself.

Comments

[wayman.livejournal.com]

Why do the largest plates have to be place on the dish drainer first? The dish drainers I'm familiar with hold the plates vertically, such that the order of small and large plates wouldn't affect stability there. Was this an artificial constraint to make the problem more Hanoi-like?

[jere7my.livejournal.com]

Why do the largest plates have to be place on the dish drainer first?

It's to maximize space in the drainer. If the small plates are behind the large plates, there're wasted corners back there that are too small to hold anything themselves, but, adjacent to larger spaces, could profitably be used to hold parts of glasses or whatnot.

[miraling.livejournal.com]

So cute!

[skalja.livejournal.com]

Tower of what?

[jere7my.livejournal.com]

Silly rabican! The Towers of Hanoi is a classic mathematical puzzle, which you can puzzle over yourself with this JavaScript version (http://www.farfarfar.com/games/towers_of_hanoi/), or read about on Wikipedia (http://en.wikipedia.org/wiki/Tower_of_Hanoi).