A cube is divided into 729 identical cubelets. Each cut is made parallel to some surface of the cube . But before doing that the cube is coloured with green colour on one set of adjacent faces ,red on the other set of adjacent faces, blue on the third set. So, how many cubelets are there which are painted with exactly one colour?

• total cubes created are 729
  
  so a plane of big cube has 9*9 cubes
  
  out of that(n-2)*(n-2)=7*7=49 are painted only one side
  
  and a cube has six sides=6*49=294
• 10 years agoHelpfull: Yes(41) No(11)
• just made a cube of 9cm as side then volume =729 cm^3 then form cubelets of 1cm^3 then we hav 729 cubes
  
  paint the adjacent sides with three colours
  now draw 4 lines of 7cm on every side of the cube
  consider RED (with 2 adjacent faces)
  then we can form 49 cubes of red on one face and another 49 cubes on another red face and at the joint of two red faces we can form 7 cubes having same colour on 2 faces then =>49+49+7=105
  
  similarly for the other two colours also. Then total cubes are 315 (105*3)
• 10 years agoHelpfull: Yes(10) No(6)
• For 1 side painted 6(n-2)^2
  n=no of sides(i.e 729=9^3)
  so n=9;
  6(9-2)^2=c*7*7=294
  
• 10 years agoHelpfull: Yes(10) No(3)
• total cube is 729.
  for one colour on one side is 7*7=49
  for 6 side 49*6=294 and adjacent side cube 7*3=21
  total one colour cube is 294+21=315
• 10 years agoHelpfull: Yes(4) No(2)
• Total Cubes=Cubes at center of each faces+cubes at corners(Except those at corners)
  = 7*7*6 + 7*3
  = 294+21= 315
• 10 years agoHelpfull: Yes(4) No(5)
• solutions by NIKHIL,RAJ ,JITENDER RAWAT is correct. Because the question states "how many cubelets are painted with EXACTLY ONE COLOUR". 294 will hold good when the question states "how many cubelets are painted with ONE COLOUR ON EXACTLY ONE FACE".
• 8 years agoHelpfull: Yes(4) No(2)
• no cubes painted on 1 side =6*(n-2)^2=6*7*7=294
  no cubes paineted on two sides with same color= 7 in adjacent faces.
  and there are 3 adjacent faces 7*3=21
  hence total no cubes painted with exactly one color 294+21=315
• 10 years agoHelpfull: Yes(2) No(1)
• 7*7*6=294
  there is 6 faces in cube .and each face consist 7*7 cube with single colour.
• 10 years agoHelpfull: Yes(1) No(2)
• 294+21=315
• 7 years agoHelpfull: Yes(1) No(1)
• n=9
  for one side paint =6*[(n-2)*(n-2)]
  =6*7*7 = 294
• 8 years agoHelpfull: Yes(0) No(1)
• 729 is the cube of 23. therefore, there are 23 length wise, 23 breadth wise and 23 height wise cuts. 23*6*2=276 dual or trial colored dices. Single colored are 729-276=453.
• 7 years agoHelpfull: Yes(0) No(2)
• given total cubes = 729 i.e. x^3 = 729
  x=9
  for 1 side painted, formula is 6(x-2)^2 = 6(7)(7) = 294
  And there are 3 adjacent corners. So, 7*3 = 21
  total is 294+21 = 315
• 6 years agoHelpfull: Yes(0) No(0)