superprismatic Posted August 17, 2009 Report Share Posted August 17, 2009 The numbers from 1 to 12 are written on the faces of a cube, two numbers to a face, in such a way that the sum of the numbers on any face is the same as the sum of the numbers on the opposite face. One of the numbers on the top face is selected, the cube rolled 90 degrees so that one of the adjacent faces comes on top, a number selected from this face, etc. The sequence 2, 1, 5, 3, 4, 7, 2, 10, 6, 11, 8, 9, 12, 3, 11, 9, 10, 7, 11, 12, 4, 1, 6, 5, 7 is generated in this manner. How are the numbers arranged on the face of the cube? Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted August 17, 2009 Author Report Share Posted August 17, 2009 The numbers from 1 to 12 are written on the faces of a cube, two numbers to a face, in such a way that the sum of the numbers on any face is the same as the sum of the numbers on the opposite face. One of the numbers on the top face is selected, the cube rolled 90 degrees so that one of the adjacent faces comes on top, a number selected from this face, etc. The sequence 2, 1, 5, 3, 4, 7, 2, 10, 6, 11, 8, 9, 12, 3, 11, 9, 10, 7, 11, 12, 4, 1, 6, 5, 7 is generated in this manner. How are the numbers arranged on the face of the cube? The word "face" in the last sentence should be "faces" Quote Link to comment Share on other sites More sharing options...
0 bushindo Posted August 17, 2009 Report Share Posted August 17, 2009 The word "face" in the last sentence should be "faces" Any day that I can solve a Walter Penney puzzle without having a crash course in group theory or berlekamp factorization algorithm is a good day. Top : 1, 9 Bottom: 3,7 Left: 6,8 Right: 2,12 Front: 4, 11 Back: 5, 10 Quote Link to comment Share on other sites More sharing options...
0 superprismatic Posted August 17, 2009 Author Report Share Posted August 17, 2009 Bushindo has it! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 18, 2009 Report Share Posted August 18, 2009 My answer... The only relevant question is what are the opposite faces/sides; since any number can be moved 90 degrees to hit another number except the opposite side. So the sides are as follows: 10/5 opposite of 11/4; 6/8 opposite of 2/12; 3/7 opposite of 1/9 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 18, 2009 Report Share Posted August 18, 2009 Two hours, pencil and paper, large eraser, three tables, looking for the next clue, and finally disproving 2 what-if's. Great puzzle, and would love another one. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 18, 2009 Report Share Posted August 18, 2009 Two hours, pencil and paper, large eraser, three tables, looking for the next clue, and finally disproving 2 what-if's. Great puzzle, and would love another one. If you start with the number 11, which appears three times in the list it helps cut the time down-- not as many what-ifs to chase Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted August 19, 2009 Report Share Posted August 19, 2009 If you start with the number 11, which appears three times in the list it helps cut the time down-- not as many what-ifs to chase Good point. That thought came to me halfway through. But since I thoroughly enjoyed the process ... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 24, 2009 Report Share Posted August 24, 2009 7 also appears three times in the list so after finding the 2 possibilities with 11, there are only 2 possibilities with 7 so only 4 combinations to work out. And, one of the four has the number 1 on 2 different sides and another has no possible solution for the remaining 2 sides so in reality only two cases to test. Quote Link to comment Share on other sites More sharing options...
Question
superprismatic
The numbers from 1 to 12 are written on
the faces of a cube, two numbers to a
face, in such a way that the sum of the
numbers on any face is the same as the
sum of the numbers on the opposite face.
One of the numbers on the top face is
selected, the cube rolled 90 degrees so
that one of the adjacent faces comes on
top, a number selected from this face,
etc. The sequence 2, 1, 5, 3, 4, 7, 2,
10, 6, 11, 8, 9, 12, 3, 11, 9, 10, 7,
11, 12, 4, 1, 6, 5, 7 is generated in
this manner. How are the numbers
arranged on the face of the cube?
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