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Problem 394

Geometry Difficulty 2.6 Multiple choice CEMC Fermat · Canada · 2026

Each of the three nets shown is folded to create a cube.

The three cubes are then arranged so that the numbers on their top
faces are $1$ , $2$ and $3$ , in some order. The sum of the three
numbers on their bottom faces is

Pick one

Official solution

If the number on the top face is a $1$ , the cube is formed from the net shown
below since it is the only net that contains the number $1$ . When this net is folded, the number on
the face opposite either of the $1$ s
is $3$ .

[[IMAGE0]]

Of the remaining two nets, the net shown below is the only net that
contains the number $3$ . Thus if the
number on the top face is a $3$ , the
cube is formed from this net. When this net is folded, the number on the
face opposite either of the $3$ s is
the other $3$ .

[[IMAGE1]]

If the number on the top face is a $2$ , the cube is formed from the remaining
net shown below. When this net is folded, the number on the face
opposite the $2$ is $8$ .

[[IMAGE2]]

Therefore, the sum of the three numbers on the bottom faces is $3+3+8=14$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.