GK 2020 Q16
16. Twelve coloured cubes are arranged in a row. There are 3 blue cubes, 2 yellow cubes, 3 red cubes and 4 green cubes but not in that order. There is a yellow cube at one end and a red cube at the other end. The red cubes are all together within the row. The green cubes are also all together within the row. The tenth cube from the left is blue. What colour is the cube sixth from the left?
- A green
- B yellow
- C blue
- D red
- E red or blue
Grey Kangaroo 2020, Question 16. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A green
We are told there is a red cube at one end and that the three red cubes are all together within the row. Therefore there is a block of three red cubes at one end. If they were at the right-hand end, the tenth cube from the left would be red. But the tenth cube from the left is blue. Hence the red cubes are at the left-hand end and a yellow cube is at the right-hand end, with a blue cube in the tenth place from the left, as shown in the diagram.
| R | R | R | B | Y |
The four green cubes are all together within the row and hence are somewhere between the 4th and 9th positions from the left. Whether they start at position 4 or 5 or 6 from the left, the cube in the 6th position from the left is green.
Solution © UK Mathematics Trust, from the GK 2020 solutions.