Each of the 12 edges of a cube is coloured either red or green. Every face of the cube has at least one red edge. What is the smallest number of red edges?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Part C (8 credits each)
Each of the 12 edges of a cube is coloured either red or green. Every face of the cube has at least one red edge. What is the smallest number of red edges?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

## Solution

If the heavy black lines represent the colour red, every face will have exactly one red edge. So the smallest number of red edges is 3 .

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-462.jpg?height=309&width=309&top_left_y=1862&top_left_x=1385)

ANSWER: (B)

## Part C