## Tuesday, April 21, 2009

### Cheese and brownies

Don't you just love crispy brownie edges and hate mushy characterless middle squares? One of my favorite gift stores, www.ThinkGeek.com , came up with an interesting brownie pan design allowing each brownie square to have at least two edges.

For cheese, it is rather the opposite. Many of us spend a lot of time at the cheese counter trying to select a piece with the minimal amount of dense wax-ed edges and more soft sides. So, here is the puzzle, suggested by one of our best puzzle solvers, Amy, and reinterpreted by me into a culinary domain:

Store receives a cube of cheese, each side is 40 inches long. Cube is covered with a thick layer of wax. Cheese seller needs to cut this cube into little cubes, each with 10 inch sides. How many premium pieces without any wax will he get? How many cubes with one waxy side, two sides and three sides?

Amy said...

Is nobody going to answer? Oh, well! I'll give this another day and then I will explain it. By the way, I love that brownie pan!

rachel_t said...

After it is cut, it will be 4 cubes wide x 4 cubes tall x 4 cubes deep, so there will be 64 cubes.

looking at the different layers of cubes below shoes of many sides of each cube will have wax:

top 2nd 3rd bottom
3223 2112 2112 3223
2112 1001 1001 2112
2112 1001 1001 2112
3223 2112 2112 3223

Cubes with 3 sides of wax: 8
Cubes with 2 sides of wax: 24
Cubes with 1 side of wax: 24
Cubes with no wax: 8

Maria said...

Wow! Rachel is leading our Family Puzzle Marathon with 5 solved puzzles.
This was a great puzzle, Amy. Thank you so much for sharing.

Michael said...

He will get 8 without wax. 24 with one wax side. 24 with 2 wax sides. 8 with three sides.