How many cuts do we need to break a 3x3x3 cube into 27 1x1x1 cubes?
A cut may go through multiple pieces.

• I think the problem asks for the minimum number of cuts required..
  In my opinion only 4 cuts are sufficient..Though it is not very easy to explain the solution of such kind of problem without the assistance of a suitable figure ,still I'm trying to reason out properly.
  
  Consider any face. We just need 2 cuts with depth =3 units at distances 1 unit and 2 units ,where the distance is measured along any edge of the face considered.
  Thus we get 3 pieces which are still form a cube 0f 3*3*3.
  
  Now, choose a 2nd face in such a way so that the chosen face lies perpendicular to the previously chosen face.And then perform an exactly similar cutting operation,i.e, in this case also 2 cuts are required.
  Consequently,we get 27 number of 1x1x1 cubes with performing only (2+2)=4 cuts.
  Still I'm not enough sure whether 4 cuts are minimum number of cuts necessary in this context to achieve the required result, so plse don't hesitate or forget to share ur feedback in this regard.
  
  Thanks to all..:-) :-)
• 12 years agoHelpfull: Yes(13) No(3)
• 6 cuts are needed.
  2 in each dimension/plane
  .
• 12 years agoHelpfull: Yes(3) No(5)
• 6
  as we divide the dimensions l,b,h 2times each
  => 2+2+2=6
• 12 years agoHelpfull: Yes(2) No(9)
• there are minimum six cuts required to break 3 unit cube into 1 unit cube...
  lets see how..
  we have 3*3*3 cube and we have to break it in 1*1*1 cube so
  first we needed 2 cuts may be horizontally or mau be vertically
  after 2 cuts we have 3 identical piece.
  after dat we will put these three pieces one and over other .
  and make two cuts horizontally or may be vertically according to first two cuts.
  it means if fist two cuts are horizontally den another two cuts are vertically and so on.
  after 2+2=4 cuts we have 9 identical pieces .but we have to break it in 27 pieces den put again one over another in order to get 27 pieces .and again vertically two cuts are required .
  so finally we have 27 identical piece of cube with dimension 1*1*1
  and the total number of cuts required
  2+2+2=6
  in whole procedure we required i horizontal and two vertical cuts.
  thanku you very much if u satisfied d answer.
• 12 years agoHelpfull: Yes(1) No(5)