As there were the same number of boys as girls, it is clear that the
number of children must be even, and, apart from a careful and exact
reading of the question, there would be three different answers. There
might be two, six, or fourteen children. In the first of these cases
there are ten different ways in which the apples could be bought. But we
were told there was an equal number of "boys and girls," and one boy and
one girl are not boys and girls, so this case has to be excluded. In the
case of fourteen children, the only possible distribution is that each
child receives one halfpenny apple. But we were told that each child was
to receive an equal distribution of "apples," and one apple is not
apples, so this case has also to be excluded. We are therefore driven
back on our third case, which exactly fits in with all the conditions.
Three boys and three girls each receive 1 halfpenny apple and 2
third-penny apples. The value of these 3 apples is one penny and
one-sixth, which multiplied by six makes sevenpence. Consequently, the
correct answer is that there were six children--three girls and three
boys.