Question 471259: The integers 11 through 16 are written on the 6 sides on a cube. A triple of faces that meet at one vertex shows 11, 12, 13. Another triple of faces that meet at a vertex shows 12, 15, 16. None of the pairs of numbers on opposite sides sum to 27. Which number is written on the face opposite 13?
choose the answer and explain the reason to choose your response16
The answer is not unique.
15
The configuration is impossible.
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! 13 is opposite 16.
Explanation:
Imagine the cube being a cardboard box, and
that we cut 7 of the edges and fold it out flat,
like this. The bottom face does not move.
Since 12 is common to the two given triples of faces that meet
at one vertex, let's put 12 on the bottom. Then we can
arbitrarily pick two faces adjacent to the BOTTOM to put the
11 and 13 in. I chose to put 11 in the FRONT and 13 on the
RIGHT. Then the 15 and 16 have to go LEFT and BACK. But which
way? Since no two opposite faces can have sum 27, we can only
put the 15 on the BACK and 16 on the LEFT.
So we have the answer already. That 13 has to be opposite 16.
And that leaves 14 for the TOP. The TOP and BOTTOM are
opposite faces, The RIGHT and LEFT are opposite faces,
and the FRONT and BACK are opposite faces, and none have sum 27.
Edwin
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