There are 4 cubes. They are arranged side by side. Black color is painted on the 4 cubes. 1st and 3rd cube is cut by 64 pieces and 2nd and 4th by 27 pieces.Then1) How many pieces painted only one side?2) How many pieces painted only two side?How many pieces painted only three side?

  
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jayadev sirimamilla

  • Jul 1st, 2006
 

1 side 81

2 side 60

3 side 8

Subhadip Mondal

  • Apr 18th, 2007
 

No. of Cubes painted on 1 side = 2(4*6)+2(6) = 60.
No. of Cubes painted on 2 side = 2(4*6)+2(2*6)=72.
No. of Cubes painted on 3 side = (2*8)+(2*8)=32.

hareesh

  • Jul 7th, 2007
 

there should be altogether 91 (64+27)  cubes.

1st cube..
no of cubes with no sides painted      = 8
no of cubes with 1 sides painted        = 6*(4 per side)=24
no of cubes with 2 sides painted        =8 on top+8 on bottom+8 in between
                                                              total=24
 no of cubes with 3 sides painted       =8(corners of cube) 


2nd cube
no of cubes with no sides painted      = 1
no of cubes with 1 sides painted        = 6*1=6
no of cubes with 2 sides painted        = 4*3=12
no of cubes with 3 sides painted        = 8



Total      
1 side painted cube       = 30
2 side painted cube       = 36 
3 side painted cube       = 16

0 side painted cube       =  9

GRAND TOTAL = 91

paul.anuj

  • Sep 23rd, 2009
 

No of cubes painted on one side for 1st & 3rd cube= 2[6(n-2)^2] =2[6(4-2)^2] = 48
No of cubes painted on one side for 2nd & 4th cube=2[6(n-2)^2] =2[6(3-2)^2] = 12
                                                                 Total No of cubes painted on one side = 50.

No of cubes painted on two sides for 1st & 3rd cube= 2[12(n-2)] =2[12(4-2)] = 48
No of cubes painted on two sides for 2nd & 4th cube= 2[12(n-2)] =2[12(3-2)] = 24
                                                              Total No of cubes painted on one side = 48.

No of cubes painted on three sides for every cube will always be 8.
Hence Total No of cubes painted on three sides = 8*4= 24.


1st and 3rd cube has been cut into 64 pieses which is (n*n*n) hence n=4.
2nd and 3rd cube has been cut into 27 pieces. hence n=3.

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