You are looking through a small hole at a corner of a standard six-sided playing die, as shown above. (The picture is showing that there are spots in the corners that you see. It does not imply absence of any other spots.)

Determine at least one of the faces of the die that you are seeing.

If you place a die so that the top side shows 6, then the back sides show (left to right): 4, 5, 3, 2, while the bottom side shows 1. Since 1 is represented by one dot in the middle of the side, it cannot create the above corner with any of the back sides. Therefore, the corner in the picture can only be created by two back sides and the top side showing 6 (not necessarily in the same rotational position as suggested by the labels "back" and "top").

3 and 2 are represented by dots going diagonally on the sides, and depending on their orientations, there can be different corners as solutions to the problem (in each case there are exactly two corners as possible solutions), but one side must always be 6.

Posted by lucky on 2002-10-26 06:25:06