In solving this little puzzle we are concerned with the exact
interpretation of the words used by the buyer and seller. I will give
the question again, this time adding a few words to make the matter more
clear. The added words are printed in italics.
"A man went into a shop to buy chestnuts. He said he wanted a
pennyworth, and was given five chestnuts. 'It is not enough; I ought to
have a sixth _of a chestnut more_,' he remarked. 'But if I give you one
chestnut more,' the shopman replied, 'you will have _five-sixths_ too
many.' Now, strange to say, they were both right. How many chestnuts
should the buyer receive for half a crown?"
The answer is that the price was 155 chestnuts for half a crown. Divide
this number by 30, and we find that the buyer was entitled to 5+1/6
chestnuts in exchange for his penny. He was, therefore, right when he
said, after receiving five only, that he still wanted a sixth. And the
salesman was also correct in saying that if he gave one chestnut more
(that is, six chestnuts in all) he would be giving five-sixths of a
chestnut in excess.