(Moved up since it's solution time.)
So while we're doing the post-mortem on this last puzzle, here's a simpler one. Someone gives you a bandsaw and a cube of wood and asks you to cut it into 27 smaller, identical cubes -- as if you had a Rubik's cube:
and wanted to slice it into its 27 smaller component cubes.
Now, it's obvious that you can do this with six cuts -- two in each dimension -- that solution's trivial. But let's say that, after each cut, you get to reorganize and re-orient your current pieces of wood before making the next cut, to try to maximize the effect of each cut.
How few cuts will you need? And, once again, hold off with the solutions until everyone gets their shot at it.
OPEN FOR SOLUTIONS: OK, feel free to post solutions. And my apologies to the previous commenter whose solution I deleted. I thought I could just undelete it but, apparently, there is no way to undelete comments. My bad.
Dammit! I come to work Monday morning and I see this! You're gonna get me fired!
must...work...don't sketch diagrams...
Nasty. I think I have a solution here; I'll hold off posting it for a bit to let others try. You are a sick, sick man. :P
Okay, I'll put myself out here again with the wrong answer but the first answer.
Here's my thinking:
1. We need a total of 27 pieces at the end of the project.
2. We start with one piece.
3. Each piece, when cut, cannot be cut into more than two pieces.
4. If we cut every single piece, every time, we cannot more than double the number of pieces with the cut.
5. 2^4 = 16, and 2^5 = 32.
Thus fewest possible number of cuts is 5; any fewer and there's no way to get the requisite number of pieces.
But really, you'd be better taking your time. Safety first when you're working with bandsaws.
Sorry if my slow work towards the answer is a little painful to those who actually, y'know, know something about math...
I'll let one of the previous commenters deal with this one.
As I said before this one is nasty, but the solution comes out pretty.
You're trying to make a 3x3 set of cubes. Look at the center cube. It has six sides. Each side must be made by cutting. If you have a saw that can cut two different sides of the same small cube at once, I want it, but you're not allowed to use it for this puzzle. So the answer is six cuts; it simply doesn't get any better than doing it the boring way.
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