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MathNet 2013 Question 95

Math Olympiad Vault · MathNet 2013

Question 95

Patrícia wants to write digits on the faces of two wooden cubes so that any day of a month can be represented by placing one face of each cube side by side. For example, to represent the first day, she places the cubes to show:
Question illustration
To represent day 26, she arranges the cubes to show:
$$2\ \mathbf{2}\ \mathbf{6}$$
Digit 6 may represent 9 by rotating the face. Remember that month days range from 01 to 31.
a) Which digits must be written on both cubes?
b) Find the digits to be written on each cube.