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Magic Cubic (Posted on 2005-11-28) Difficulty: 2 of 5
Number the corners of a cube from 1 to 8, so that the sum of the four corners of every face is the same.

No Solution Yet Submitted by sragen    
Rating: 2.6667 (6 votes)

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Working Out | Comment 8 of 14 |

The solution has been posted but perhaps some people won't know how to get there.   So, here is an easy way to work out this puzzle:

When assigning numbers to corners you should try to balance diametrically opposite sides - eg put 8 on one corner (front face)and on the diametrically opposite corner a 7(rear face), then put the 1 on a corner on the front face, to balance this put a 2 on a corner on the rear face.   Carry on similarly with the rest of the numbers.

You'll end up with something like this:

Front face starting at top left hand corner working clockwise:  8 1 5 4

Rear face starting at top left hand corner working clockwise:  6 3 7 2

The faces don't add up so try to balance -in this case all faces =18 except two of them, which come to 20 and 16.   ie the 20 face needs to lose 2 points and the 16 face has to gain 2 points.

This is easily achieved by swapping the 6 with the 3 and swapping the 4 with the 5.

Now all faces have a sum of 18.   QED

  Posted by MSH on 2006-03-24 14:43:48
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