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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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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"

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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

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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

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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. B))

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

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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.

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