IMC 2014 Q8
8. A large cube is made by stacking eight dice. The diagram shows the result, except that one of the dice is missing. Each die has faces with 1, 2, 3, 4, 5 and 6 pips and the total number of pips on each pair of opposite faces is 7. When two dice are placed face to face, the matching faces must have the same number of pips. What could the missing die look like?
Intermediate Mathematical Challenge 2014, Question 8. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C
The missing die, if correctly placed in the figure, would show faces 1, 3, 5 placed in a clockwise direction around the nearest corner. An examination of each of the five proposed dice shows that only C has this property.
Solution © UK Mathematics Trust, from the IMC 2014 solutions. Longer versions with investigations: Solutions and investigations (PDF).