[Prof. Templeton]

After stealing Bonanova’s puzzle theme, our industrious puzzle-loving waiter has also taken the plates from his previous riddle and placed them back on the circular table from the first riddle.

Twelve plates are evenly spaced around the edge of a circular table and a diner roll is placed on each plate.

Starting at any plate you like and going in one direction only, your job is to pick up a roll and pass it over two other rolls before placing it back on a plate.

Only six rolls should be moved, six plates should end empty and six plates should end with two rolls on them. If you return to where you started, what is the minimum number of full revolutions needed to complete the task.

[HoustonHokie]

Clarification request:

1. Does passing a roll over a plate that already has two rolls count as passing over 1 or 2 rolls?

1a. If consecutive plates have 1, 1, & 2 rolls respectively, can a roll be picked up from the first plate and moved beyond the plate with 2 rolls?

2. Does the waiter have to set the roll down on the next plate following the plate with the second roll, or can he keep moving with the roll, provided he does not pass over a third roll? In other words, if you pass over two rolls and the next plate is empty, does the waiter have to set the roll down on the empty plate, or can he move it to a plate that's not empty?

Edited February 9, 2009 by HoustonHokie

[Prof. Templeton]

Clarification request:

1. Does passing a roll over a plate that already has two rolls count as passing over 1 or 2 rolls?

1a. If consecutive plates have 1, 1, & 2 rolls respectively, can a roll be picked up from the first plate and moved beyond the plate with 2 rolls?

2. Does the waiter have to set the roll down on the next plate following the plate with the second roll, or can he keep moving with the roll, provided he does not pass over a third roll? In other words, if you pass over two rolls and the next plate is empty, does the waiter have to set the roll down on the empty plate, or can he move it to a plate that's not empty?

(1.)Two rolls are two rolls no matter where they are.

(1a)No, you can pass over two rolls only.

(2)You can pass as may empty plates as you like.

[HoustonHokie]

Assuming the answer to my question #2 above is "no" (ahh, I see the answer now - thanks), I think I can do it in 3 trips around the table. Here's how:

Original: 1 1 1 1 1 1 1 1 1 1 1 1

1st Rev: 0 1 1 2 0 1 1 2 0 1 1 2

2nd Rev: 0 1 0 2 0 2 0 2 0 2 0 2 (only 11 rolls because 1 is in the waiter's hand)

3rd Rev: 0 2 0 2 0 2 0 2 0 2 0 2

Edited February 9, 2009 by HoustonHokie

[Prof. Templeton]

Assuming the answer to my question #2 above is "no" (ahh, I see the answer now - thanks), I think I can do it in 3 trips around the table. Here's how:

Original: 1 1 1 1 1 1 1 1 1 1 1 1

1st Rev: 0 1 1 2 0 1 1 2 0 1 1 2

2nd Rev: 0 1 0 2 0 2 0 2 0 2 0 2 (only 11 rolls because 1 is in the waiter's hand)

3rd Rev: 0 2 0 2 0 2 0 2 0 2 0 2

3 is the minimum. 4 trips is usually much easier to visualize.