GeekDad Puzzle of the Week Solution: Waffle Cuts

Reading Time: 2 minutes

Nora, and a WaffleNora, and a WaffleThis week’s puzzle, while delicious, caused quiet a bit of confusion and a few rather interesting answers. Here is the puzzle as presented:

This morning as I was making both Max and Nora breakfast, I noticed that while their meals were rather similar in content and form, they were quite different in their divisibility. Max’s French Toast (or “pain perdu,” as he prefers to call it) can be cut an infinite number of ways, as I could vary the cuts both in width/height, as well as angle. Nora’s waffle, with its rigid lines at right angles, can only be cut a finite number of different ways.

So this week’s GeekDad Puzzle of the Week came to me in a flash: just how many different ways could Nora’s waffle be cut?

Using one of her waffles, I traced the diagram, below. (Please excuse the syrup!) As you can see, and for the purposes of this puzzle, a waffle is a circular shape truncating a grid. Each of the middle rows/columns have 7 “segments,” along the edges of which a cut can be made. Each succeeding row or column has one fewer “segment,” with only 5 squares of syrup gathering goodness at the edge.

wafflewaffle

If we cut only at these edges, and if each cut traverses the waffle in a straight line from edge to edge, how many different ways can the waffle be cut? I will count rotations, horizontal flips, and vertical flips of cut sets as the same “set” of cuts.

It turns out that, including the “no cuts at all” solution, there are some 666 different ways to cut Nora’s waffle. (For those that are hexakosioihexekontahexaphobic, please understand that I don’t always have the solution in hand when I post the puzzle!)

Congratulations to Rich Collum for correctly answering this week’s puzzle and being the winner of the $50 ThinkGeek gift certificate. For everyone else, please use the code GEEKDAD68JH to get $10 off an order of $50 or more at ThinkGeek.

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