August 17, 2010

3x3x3 wooden cube

Imagine a 3x3x3 wooden cube.

How many cuts do we need to break it into 27 1x1x1 cubes?

6 if you keep the cube togheter after every cut.

If after the first cut you consider each part a seperate one you'll need 26 cuts

Anonymous said...

6

drblast said...

Five cuts.

Cut off one third of the cube. Lay that piece horizontally on top of the remaining piece, and cut through both.

You now have four pieces, a 1x1x3, a 1x2x3, and two 1x3x3's. Lay them flat on the table and arrange them to form a 1x3x9 grid. Cut 1/3rd off lengthwise.

Now set the one 1x1x1 block aside and arrange the rest to form a 2x13 grid, and cut that in half lengthwise.

Then, spin all blocks 90 degrees and arrange them into a transposed 13x2 grid, making the final lengthwise cut.

Occum said...

Just 4 cuts

two cuts laterally and two cuts horozontally keeping it all together and producing 3x3x3 or...27

DoubleBouble said...
This comment has been removed by the author.
Anonymous said...

@ occum then you have 9 stris of 1x1x3

Anonymous said...

With anything fewer than 6 cuts, how does the center cube (which as a fresh cut for every surface) get cut free?