April 28th, 2018, 10:00 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  Please explain the solution.
A Cube is decorated in such a way that one diamond is placed at each corner, 6 diamonds are placed at each edges and 3 diamonds are placed at the center of each face. How many diamonds are there on the cube? Solution: No of units = (E  2C) 12 Corner = 8 X 1 = 8 Edges = (E2C) 12 = (5  2X1)8 = 36 Face = 6 x 3 = 18. My friend showed me a solution to this problem and hesitate to explain it. please help me. Last edited by skipjack; April 28th, 2018 at 10:54 PM. 
April 28th, 2018, 11:02 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,530 Thanks: 1750 
There are inconsistencies. The description states that 6 diamonds are placed on each edge, but the solution uses E = 5. Also, the solution incorrectly changes 12 (the number of edges) to 8. In the description, it's unclear whether the number of diamonds placed on each edge includes the diamonds at the ends of each edge (the corner diamonds). If the 6 diamonds placed on each edge include 2 corner diamonds, the total number of diamonds is given by 8 × 1 + 12 × (6  2) + 6 × 3 = 74, because there are 8 corners, 12 edges and 6 faces. 

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