OT - Tower of Hanoi

[Chuck]

Somewhere down the message list here was a conversation about the TofH game. I had my Intermediate Algebra students discover the pattern; calculate the number of moves for 70 disks; and the time it would take to solve it making 1-trillion moves per second (a long time).

It got me thinking (but not too much yet), what if the rules were the same, but at any step you could move 2 disks. But why stop there? How many moves will it take to solve using "m" disks if you can move at most "n" at any time? Hmmmm.

I should probably do a search on this before pressing send, but it's more fun to ponder it awhile.

[Allen]

The first few chapters of Knuth's Concrete Mathematics explores pretty much any variation of ToH that you might like.

Without much thought, being able to move two disks of a 70-disk stack seems like it would play much like a 35 disk stack without much change in complexity.

[Crawl]

Almost simultaneous posts!

The way I thought the new rule worked was that you just can move two pieces per turn, hence you halve the number of moves.

I think the way you thought of it was that any two stacked pieces can be moved at once as a single piece, which acts like halving the number of pieces.

[Crawl]

Can you explain why allowing 2 disks to be moved in one step would have any effect other than halving the number of steps total?

[Patrice]

Hi,

My first guess (a 2 seconds thinking) is that:

a ToH of 30 disk with a move of 2 disks at the time is the same as a ToH of 15 disks.

a ToH of 30 disk with a move of 3 disks at the time is the same as a ToH of 10 disks.

Patrice

[Chuck]

[bashful]Yup, like I said, didn't think about it much.[\bashful] Too much on my mind to have thought rationally for more than a second.

Edited: 18 Nov 2010, 8:40 p.m.