American University Rubik's Cube Fill-in Problem

Did the problem that appeared in an oral exam at the University of Washington (USA) in 2011 give you a hard time?

Given a rubik's cube with dimensions as shown in the figure:

Each face of the Rubik's Cube is a 2x2 square divided into four 1x1 squares. Two 1x1 squares are called "neighbors" if they share exactly one edge (and thus, each 1x1 square has exactly four neighbors).

Alex wants to fill in 1x1 squares, one integer per square, so that the sum of each number and its four neighbors is 13. Can Alex do this? If so, explain how he filled in the numbers; if not, explain why.

>>See solution

Vo Quoc Ba Can
Math Teacher, Archimedes School Hanoi

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