Est. 1998 — 27 years of woodworking knowledge
Tuesday Puzzle
You are given a 3x3x3 cube, and asked to saw it into 9 1x1x1 cubes. One obvious way involves six cuts, two in each dimension, leaving the cut pieces stacked together as in the original cube. But is it possible to accomplish this task in fewer than six cuts, by rearranging the pieces after each cut, to maximize the effect of subsequent gang cuts?
Re: Tuesday Puzzle
It's a trick question. Due to the kerfs, it's impossible to get 9- 1X1 cubes! ;-)
Tom
Make that 3.25x3.25 to start ;-)
I get 4 cuts by
cutting the original into thirds. Then stacking those three pieces on top of one another. Then cutting that "board" into thirds.
That WOULD work
if the goal were to create 1x1x3 pieces. Unless I am picturing wrong what you are suggesting.
Re: Tuesday Puzzle
With 5 cuts you get 9, with 6 you get 27. ;)
:-)
Stupid puzzle statement error
Doh! I meant to say cut the 3x3 cube into _27_ 1x1 cubes.
Ed has correctly pointed out that you can get 9 1x1 cubes (as asked in the original question, but I'm too honest to claim that I did that on purpose as a trick question, although it would be a good one!) with five cuts. But can you get 27 with any fewer than 6 cuts?
Re: Tuesday Puzzle
Four cuts (but have to stretch the definition of a cut).
Suppose you make the first two cuts to yield 3 pieces, each 1x3x3.
For 3rd cut, lay these flat so that you have a 1x9x3 piece to push through saw. As the cut proceeds, you can pick up the resulting 1x3x3 and 2x3x3 pieces and place them at back of the line, while still continuing this cut. So initially you are cutting 1x3x3 pieces, but as the cut continues you are cutting 1x1x3 and 1x2x3 pieces. At end of this cut you will have 3 1x1x1 pieces, 6 1x1x2 pieces, and 3 1x2x2 pieces.
Line up the 1x2x2 pieces, followed by the 1x1x2 pieces and start the 4th cut. As the 1x2x2 pieces come off the saw, add to the back of the line. When you finish this cut, all the pieces will be 1x1x1.
Re: Stupid puzzle statement error
The centre cube, surrounded by the other 26 pieces, has 6 cut faces.
But first a word about shop safety ;-)
VERY creative! I think with this approach you could do it with just two "cuts", continuing to move uncut pieces in the path of the blade while it's "working" on other pieces.
But that's not what I had in mind. I guess that besides getting that 3^3 =27, not 9, I should have specified that I was referring to cuts with a kerfless saw, that divides the wood along a plane, and that no wood is moved during a cut!
Hurry back, Dan; I'm drowning here! ;-)
And that's the answer!
Wrong answer
You can't saw a 3 x 3 x 3 cube into 27 1 x 1 x 1 cubes. The saw kerf would reduce your final dimension by the width of the kerf. You would have to use a knife or axe to make the cuts so the wood is cleaved not sawn. You would still need to make six cuts.
Lee
Nominal measure
Thomas beat you to that one. What I really meant was nominal measure, where a 3x3x3 is a true 2.5 per side, and a 1x1x1 is a true 3/4 per side. And if you believe that one, I've got a bridge to sell you. ;-)