1

Part of 2020 May Olympiad

Problems(2)

We say that a positive integer is super odd

Source: May Olimpiad 2020 L2 P1

We say that a positive integer is super odd if all of its digits are odd. For example, 1737 is super odd and 3051 is not. Find an even positive integer that cannot be express as a sum of two super odd numbers and explain why it is not possible to express it thus.

Sofia places the dice on a table as shown in the figure

Source: May Olympiad 2020 L1 P1

Sofia places the dice on a table as shown in the figure, matching faces that have the same number on each die. She circles the table without touching the dice. What is the sum of the numbers of all the faces that she cannot see?

Note

. In all given the numbers on the opposite faces add up to 7.