*(From Brahmagupta, 7th century A.D.)* A girl was carrying a
basket of eggs, and a man driving a horse hit the basket and broke all
the eggs. Wishing to pay for the damage, he asked the girl how many
eggs there were. The girl said she did not know, but she remembered
that when she counted them by twos, there was one left over; when she
counted them by threes, there were two left over; when she counted
them by fours, there were three left over; when she counted them by
fives, there were four left; and when she counted them by sixes, there
were five left over. Finally, when she counted them by sevens, there
were none left over. `Well,' said the man, `I can tell you how many you
had.' What was his answer?