On each of the twelve edges of a cube we write the number 1 or −1. For each face of the cube, we multiply the four numbers on the edges of this face and write the outcome on this face. Finally, we add the eighteen numbers that we wrote down.
What is the smallest (most negative) result we can get? In the figure you see an example of such a cube. You cannot see the numbers on the back of the cube.
Solution
−12
Want a route through all this instead of an archive? The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.
Source: MathNet,
licensed CC-BY-4.0.
Statement and solution reproduced as published; topic and difficulty added by this site.
