Let's play dice
Logic
Level
3
The two dice in the picture are identical. They each have all of the six numbers of dots (1, 2, 3, 4, 5, 6) on their faces.
How many dots are there on the opposite face of 6?
1
3
There isn't enough information
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1 solution
Use the visual information in the photograph to construct the model of these identical dice (call left die A, right die B). Use the model to find the value of the opposite face of the face with value 6.
6 is assigned to an arbitrary face of the model. Die A tells us that 2 is adjacent to 6 and 4, and so we first assign 2 to an arbitrary face adjacent to 6. Then, 4 is assigned the face adjacent to 2 and 6 such if it were facing down, the right side of 2 would be adjacent to the left side of 6 (in accordance with the photograph). Next, Die B tells us that 5 is adjacent to 6 and 4. We assign 5 to the remaining free space adjacent to 6 and 4.
Notice that neither die gives any information about the locations of 1 and 3. Without this information, it is equally likely that either value can be assigned to either remaining face. Therefore, there is not enough information to determine the value of the opposite face of 6.
It can be argued that the value opposite of 6 must be 1 due to the configuration of dots on a standard die in which all opposite faces sum to 7. However, this problem does not introduce this constraint and therefore we can make no assumptions about which value is assigned to which face.