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 ▼ Chuck Senior Member Posts: 320 Threads: 59 Joined: Dec 2006 11-18-2010, 04:47 PM 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 Senior Member Posts: 562 Threads: 27 Joined: Oct 2006 11-18-2010, 05:16 PM 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 Senior Member Posts: 306 Threads: 3 Joined: Sep 2009 11-18-2010, 05:23 PM 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 Senior Member Posts: 306 Threads: 3 Joined: Sep 2009 11-18-2010, 05:19 PM 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 Senior Member Posts: 274 Threads: 23 Joined: Sep 2007 11-18-2010, 08:19 PM 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 Senior Member Posts: 320 Threads: 59 Joined: Dec 2006 11-18-2010, 08:38 PM [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.

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