Here is how the first few numbers would be represented in Jonah's system: 1=O, 2=X, 3=OX, 4=XOX, 5=OOOX, 6=XX.

Jonah tells Alice that he has chosen a number between 1 and N, inclusive, and that he has represented it by a 9-letter word (indicating divisibility by 2 through 10). Alice, sitting across the table, looks at the word and says that the number must be A. Jonah is puzzled because that is not the number he chose. Alice, seeing his confusion, quickly realizes what the problem is, and gives him the expected answer.

What were Jonah's and Alice's numbers?