Question

What is the least number of cuts required to cut a cube into 84 identical pieces, assuming all cuts are made parallel to the faces of the cube?

1. 11
2. 12
3. 13
4. 10

Answer 1

according to question , its asking about least number of cuts , which give 84 identical pieces ...

lets consider the case , in which its not least (for maximum ) then simply ...83 cuts ...which all are in same direction...

but you cut in (X,Y,Z) directions ...you will get minimum no of cuts ....

for eg we want 8 identical pieces ... if i cut in single direction then i have to cut it in 7 times , if i cut in X,Y direction , then 3 cut in one direction and 1 in other direction so total 4 cuts required , now if i cut in X,Y,Z directions then , 1 cut in X, 1 cut in Y, 1 Cut in Z , so total required cuts only 3 which is least ...(8= 2*2*2= (1+1)(1+1)(1+1) ) at each direction 1 cut , 2 pieces so total 8 picese using only 3 cuts .

 

Now come to the question .. 84identical pieces = 3*4*7=  here 3 using 2 cuts in X, 4 using 3cuts in Y, 7 using 6cuts in Z , 

 so totals cuts = 2+3+6= 11(least cuts) hence answer is option 1)11.

Answer 2

1.5