Mrs. Covey, who keeps a little poultry farm in Surrey, is one of the most
eccentric women I ever met. Her manner of doing business is always
original, and sometimes quite weird and wonderful. She was once found
explaining to a few of her choice friends how she had disposed of her
day's eggs. She had evidently got the idea from an old puzzle with which
we are all familiar; but as it is an improvement on it, I have no
hesitation in presenting it to my readers. She related that she had that
day taken a certain number of eggs to market. She sold half of them to
one customer, and gave him half an egg over. She next sold a third of
what she had left, and gave a third of an egg over. She then sold a
fourth of the remainder, and gave a fourth of an egg over. Finally, she
disposed of a fifth of the remainder, and gave a fifth of an egg over.
Then what she had left she divided equally among thirteen of her friends.
And, strange to say, she had not throughout all these transactions broken
a single egg. Now, the puzzle is to find the smallest possible number of
eggs that Mrs. Covey could have taken to market. Can you say how many?