The number must be the least common multiple of 1, 2, 3, etc., up to 15,
that, when divided by 7, leaves the remainder 1, by 9 leaves 3, by 11
leaves 10, by 13 leaves 3, and by 14 leaves 8. Such a number is 120. The
next number is 360,480, but as we have no record of a tree--especially a
very young one--bearing anything like such a large number of apples, we
may take 120 to be the only answer that is acceptable.