[Guest]

A wooden cube of 3'' can be cut in 27 cubes of 1'' each by the buzz saw.

Only 6 cuts of saw are necessary to do this, while keeping the pieces together

Now, can you reduce the number of cuts by rearranging the pieces after each cut?

If you can, how can it be done?

If you can't, why can't it be done?

[Guest]

No because the saw takes 3-4mm depending on the kerf, so the cubes are not therfore 1" -

if this is to be ignored...of course it can after the first cut... Lay the first 1x3 slab in front of the 2x3 slab to pass through the saw again!

I think - where's my old rubik cube!

[Guest]

A wooden cube of 3'' can be cut in 27 cubes of 1'' each by the buzz saw.

Only 6 cuts of saw are necessary to do this, while keeping the pieces together

Now, can you reduce the number of cuts by rearranging the pieces after each cut?

If you can, how can it be done?

If you can't, why can't it be done?

It cannot be done, because the largest remaining piece after each cut will always take 6 cuts to break down into 1 inch cubes. This is not affected by rearranging the smaller "offcuts" in order to cut more than one piece each time.

[Guest]

No because the saw takes 3-4mm depending on the kerf, so the cubes are not therfore 1" -

if this is to be ignored...of course it can after the first cut... Lay the first 1x3 slab in front of the 2x3 slab to pass through the saw again!

I think - where's my old rubik cube!

Yes, kerf is to be ignored.

No, even if you don't lay the first 1x3 slab in front of the 2x3 slab and still pass the saw through it, won't it be a similar situation?

[Guest]

We start with a cube of 3x3x3 (27 potential 1" cubes)

Each cut can either divide the largest remaining piece into 2 halves or 1/3 + 2/3.

So if we follow the largest remaining pieces it goes:

(apologies for the dots, it seems the forum does not like white space!)

........... 27

............ |

1 ........ (2/3)

............ |

........... 18

.......... / . \

2 ... (1/2) ... (2/3)

....... | ....... |

....... 9 ...... 12

....... | ..... /..\

3 ... (2/3)..(1/2) (2/3)

......... \../ ..... |

.......... 6 ....... 8

......... /..\ ..... |

4 ... (1/2) (2/3)..(1/2)

....... | ..... \ /

....... 3 ...... 4

....... | ...... |

5 ... (2/3) .. (1/2)

......... \ . /

............ 2

............ |

6 ........ (1/2)

............ |

............ 1

[Guest]

No, it cannot be done with fewer than six cuts.

Think about the small cube in the dead center. Initially, it has no faces because it is connected to the rest of the cube. When you're done and have 27 little cubes, this central 'chunk' of the original cube will have six faces. So there had to be six separate cuts to create those six faces on that central 'chunk' of the original cube.

Since you can't create this cube with less than six cuts, you can't possibly get 27 cubes with less than six cuts.

[rookie1ja]

apologies for the dots, it seems the forum does not like white space!

the forum likes white space - in code tags or codebox tags

			example of 

 text		in	code	tags[/code]

[Guest]

the forum likes white space - in code tags or codebox tags

Thanks     that's     so    much    easier!!!

[Guest]

Yes, you all are correct

The wood at the center needs 6 cuts to form a cube

[bonanova]

The center cube has six faces, no two of which can be formed with a single cut.