GK 2016 Q14
14. Seven standard dice are glued together to make the solid shown.
The pairs of faces of the dice that are glued together have the same number of dots on them. How many dots are on the surface of the solid?
- A 24
- B 90
- C 95
- D 105
- E 126
Grey Kangaroo 2016, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 105
A standard die has a total of 21 dots on its faces. The faces that are glued together have the same number of dots. Since the die in the centre of the solid has all its faces glued to other dice, the sum of the dots that are not on the surface of the solid is 2 × 21. Therefore, the number of dots on the surface of the solid is 7 × 21 − 2 × 21 = 5 × 21 = 105.
Solution © UK Mathematics Trust, from the GK 2016 solutions.