Sunday, June 03, 2012

GeekDad Puzzle of the Week: Waffle Cuts

GeekDad Puzzle of the Week: Waffle Cuts: Waffle, no cuts
Q: If we only cut along the ridges of a circular waffle, and if each cut traverses the waffle in a straight line from edge to edge, how many different ways can the waffle be cut?
Note: rotations, horizontal flips, and vertical flips of a set of cuts should only be counted once.
Given that there are 6 places to cut vertically and 6 places to cut horizontally, that's a total of 12 cut lines. If you allow for any combination of these 12 lines to be cut or not, you have a total of 2^12 = 4096 ways to divide the waffle. But of course, the puzzle asks for the number of unique ways to cut the waffle, not including any mirrored or rotationally symmetric sets of cuts.

After the official answer to the puzzle is posted, I'll post my solution here.

Edit: The solution is posted, but just the number without any detail. Also, I disagree with their counting of the "no cuts at all" solution as one of the ways to "cut" the waffle. In any case, a full detailing of my solution along with an enumeration of all 665 (or 666) ways to uniquely cut the waffle can be found in Blaine's Solution to the GeekDad Waffle Puzzle.

2 comments:

  1. It was not mentioned if this happens to be a Belgian waffle. If so perhaps we could take it next door and try this puzzle in the Hague.

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  2. I'd really only be guessing here, to a degree.

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