Amusements in Mathematics HTML version

Though the following little puzzle deals with the purchase of chestnuts, it is not itself of
the "chestnut" type. It is quite new. At first sight it has certainly the appearance of being
of the "nonsense puzzle" character, but it is all right when properly considered.
A man went to 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," he remarked! "But if I give you
one chestnut more." the shopman replied, "you will have five too many." Now, strange to
say, they were both right. How many chestnuts should the buyer receive for half a crown?
Here is a little tangle that is perpetually cropping up in various guises. A cyclist bought a
bicycle for £15 and gave in payment a cheque for £25. The seller went to a neighbouring
shopkeeper and got him to change the cheque for him, and the cyclist, having received
his £10 change, mounted the machine and disappeared. The cheque proved to be
valueless, and the salesman was requested by his neighbour to refund the amount he had
received. To do this, he was compelled to borrow the £25 from a friend, as the cyclist
forgot to leave his address, and could not be found. Now, as the bicycle cost the salesman
£11, how much money did he lose altogether?
"How much did yer pay for them oranges, Bill?"
"I ain't a-goin' to tell yer, Jim. But I beat the old cove down fourpence a hundred."
"What good did that do yer?"
"Well, it meant five more oranges on every ten shillin's-worth."
Now, what price did Bill actually pay for the oranges? There is only one rate that will fit
in with his statements.
"The days of our years are threescore years and ten."
Psalm xc. 10.
For centuries it has been a favourite method of propounding arithmetical puzzles to pose
them in the form of questions as to the age of an individual. They generally lend