Answer to Riddle #82: Cutting a 3-inch cube into 27 1-inch cubes
82. A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on each side, into 27 one-inch cubes. He can do it easily by making six cuts through the cube, keeping the pieces together in the cube shape. Can he reduce the number of necessary cuts by rearranging the pieces after each cut?
I got this puzzle out of a book, I like it because of it's simplicity, you can spend ages thinking about it, and then, all of a sudden...
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The answer is no, you can not reduce the number of cuts below 6. But why? Probably the easiest way to think about it is to consider the center cube.
This cube, like all cubes, has six sides. Since non of them are initially exposed, it will require six separate cuts to expose them.
The pieces can be rearranged, but there is no way of reducing the number of cuts below 6.
ChatGPT got this completely wrong Bard did a lot better.
If you're curious what Bard made of this puzzle...
No, the carpenter cannot reduce the number of necessary cuts by rearranging the pieces after each cut. The minimum number of cuts required to cut a three-inch cube into 27 one-inch cubes is six. This is because each of the six sides of the cube must be cut in order to create the 27 smaller cubes.
Here is a diagram of the six cuts that are required:
[Image of a three-inch cube with six cuts through it. The cuts divide the cube into 27 one-inch cubes.]
The carpenter could rearrange the pieces after each cut, but this would not reduce the number of cuts required. The six cuts are still necessary in order to create the 27 smaller cubes.
If you're curious what ChatGPT made of this puzzle...
The below answer IS WRONG
Yes, the carpenter can reduce the number of necessary cuts by rearranging the pieces after each cut. The key to this problem is to recognize that the carpenter does not need to make all six cuts in a specific order, and that rearranging the pieces after each cut can lead to a more efficient solution.
Here is one way the carpenter can reduce the number of cuts needed:
Make the first cut vertically through the center of the cube, dividing it into two rectangular pieces.
Take one of the rectangular pieces and make a horizontal cut through the center of the piece, dividing it into two smaller rectangular pieces.
Stack the two smaller rectangular pieces on top of each other, and make a vertical cut through the center of the stack, dividing it into two smaller rectangular pieces.
Repeat steps 2 and 3 with the other rectangular piece from step 1.
Stack the resulting four rectangular pieces on top of each other, and make a horizontal cut through the center of the stack, dividing it into two smaller rectangular pieces.
Finally, stack the two smaller rectangular pieces on top of each other, and make a vertical cut through the center of the stack, dividing it into two smaller rectangular pieces.
After these six cuts, the carpenter will have 27 one-inch cubes, and he only needed to make five rearrangements of the pieces between cuts. Therefore, the carpenter was able to reduce the number of necessary cuts from six to five by rearranging the pieces after each cut.
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