0
$\begingroup$

is following step right proving?

it is first time I prove something so I am wonder whether it is right or wrong.

---given problem---

there is a cube whose one side is 3 inch long.

a person cuts 6 times for making 27 cubes whose one side is 1 inch long.

is there a way to cut less than 6 times for making 27 cubes?

if not, prove it.

---proving---

for any shape of object,

for making one or more cube, I should cut 6 times

because only one plane would be made for each cut.

and cube have 6 plane.

making 27 cubes is more than making a cube.

so making 27 cubes require at least cutting 6 times which time is times of cutting for making a cube.

I tried to prove "for making one or more cube, it require cutting at least 6 times"

does it same as proving "there is no way to make 27 cube with cutting less than 6 times"?

thanks!

  • 3
    If you are referring to the little cube inside, then this sounds good to me. That cube doesn't share any of its faces with the big 3x3x3 cube, and a single cut cannot produce more than one face, as you said (I think?)2011-07-22
  • 1
    If I want to make 8 cubes, I only need to cut 3 times. But your argument would still suggest cutting 6 times because "making 8 cubes is more than making a cube". So there is something missing in your argument.2011-07-22
  • 1
    (And the missing thing is in Jyrki's comment, which I didn't see before posting...)2011-07-22
  • 1
    The way I saw Jyrki's comment expressed originally was to think of painting the exterior of the original cube. The inner cube has no paint, so needs 6 cuts, no matter how you rearrange the pieces between cuts. This distinguishes the 3x3x3 case from the 2x2x2 case.2011-07-22
  • 0
    I quite like Ross's use of paint here. Admittedly my choice of phrase "shares a face" is not quite as precise as we might like it to be, but at least you understood.2011-07-23

1 Answers 1