1998 CEMC Gauss (Grade 7) Problems/Problem 20

Problem

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?

$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 6$

Solution

Let the vertices of the cube be $ABCDA_1B_1C_1D_1.$ Shade $AD$ , $CC_1,$ and $A_1B_1.$ That way, every face contains at least one red edge, and the answer is $\boxed{\text{(B)}}.$

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1998 CEMC Gauss (Grade 7) Problems/Problem 20

Problem

Solution