An old woman, carrying eggs to market in a basket, met an unruly fellow, who broke them. Being taken before a magistrate, he was ordered to pay for them, provided the woman could tell how many she had; but she could only remember, that in counting them into the basket by twos, by threes, by fours, by fives, and by sixes, there always remained one; but in counting them in in by sevens, there were none remaining. Now, in this case: how was the number to be ascertained ?

This is the same thing as to find a number, which being divided by 2, 3, 4, 5, and 6, there shall remain 1, but being divided by 7 there shall remain nothing; and the least number, which will answer the conditions of the question, is found to be 301, which was therefore the number of eggs the old woman had in her basket.