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August 17, 2010

3x3x3 wooden cube

Imagine a 3x3x3 wooden cube.

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


André Meneses said...

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...


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?

Prasad said...

Only 4 Cuts required.

2 on one side and other 2 on it's perpendicular side, keeping cubes together till final cut..