Library / /386 of 482

, 2014

Combinatorics Difficulty 2.4 Junior Find the answer Canada

Two cubes are stacked as shown. The faces of each cube are labelled with 1, 2, 3, 4, 5, and 6 dots. A total of five faces are shown.

What is the total number of dots on the other seven faces of these two cubes?

Pick one

Solution

Solution 1

The faces not visible on the top cube are labelled with 2, 3 and 6 dots.

The faces not visible on the bottom cube are labelled with 1, 3, 4, and 5 dots.

Thus, the total number of dots on these other seven faces is $2+3+6+1+3+4+5=24$ . Solution 2 Since each of the two cubes has faces labelled with 1, 2, 3, 4, 5, and 6 dots, then the total number of dots on the two cubes is $2 \times (1+2+3+4+5+6)=2 \times 21=42$ . The five visible faces have a total of $4+1+5+6+2=18$ dots. Therefore, the seven other faces have a total of $42-18=24$ dots.

Figure for this problem

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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