olymmath

KöMaL 2022 C1737

    Dick got two dice for his 32th32^\text{th} birthday. He labelled the faces of one die with the numbers 1,2,…,61, 2, \ldots, 6, and the faces of the other one with 0,1,2,7,8,90, 1, 2, 7, 8, 9. By using these dice, he can form all integers from 10 up to his age, 32, but the next number, 33, cannot be formed. Octavia uses two regular octahedra instead. Similarly, she wrote a digit on each face of both octahedra, so she can also form all integers from 10 up to her current age (in years), but not the next one. How old is Octavia now?

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