“I am sure you are all wrong,” insisted Mr. Wilson, “for I consider that Eve 8 1 4 Adam, and Adam 8 1 2 4 Eve, so we get a total of 8,938.”

“But, look here,” broke in Herbert.  “If Eve 8 1 4 Adam and Adam 8 1 2 4 2 oblige Eve, surely the total must have been 82,056!”

At this point Uncle Walter suggested that they might let the matter rest.  He declared it to be clearly what mathematicians call an indeterminate problem.

100.—­THE LABOURER’S PUZZLE.

Professor Rackbrane, during one of his rambles, chanced to come upon a man digging a deep hole.

“Good morning,” he said.  “How deep is that hole?”

“Guess,” replied the labourer.  “My height is exactly five feet ten inches.”

“How much deeper are you going?” said the professor.

“I am going twice as deep,” was the answer, “and then my head will be twice as far below ground as it is now above ground.”

Rackbrane now asks if you could tell how deep that hole would be when finished.

101.—­THE TRUSSES OF HAY.

Farmer Tompkins had five trusses of hay, which he told his man Hodge to weigh before delivering them to a customer.  The stupid fellow weighed them two at a time in all possible ways, and informed his master that the weights in pounds were 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121.  Now, how was Farmer Tompkins to find out from these figures how much every one of the five trusses weighed singly?  The reader may at first think that he ought to be told “which pair is which pair,” or something of that sort, but it is quite unnecessary.  Can you give the five correct weights?

102.—­MR. GUBBINS IN A FOG.

Mr. Gubbins, a diligent man of business, was much inconvenienced by a London fog.  The electric light happened to be out of order and he had to manage as best he could with two candles.  His clerk assured him that though both were of the same length one candle would burn for four hours and the other for five hours.  After he had been working some time he put the candles out as the fog had lifted, and he then noticed that what remained of one candle was exactly four times the length of what was left of the other.

When he got home that night Mr. Gubbins, who liked a good puzzle, said to himself, “Of course it is possible to work out just how long those two candles were burning to-day.  I’ll have a shot at it.”  But he soon found himself in a worse fog than the atmospheric one.  Could you have assisted him in his dilemma?  How long were the candles burning?

103.—­PAINTING THE LAMP-POSTS.

Tim Murphy and Pat Donovan were engaged by the local authorities to paint the lamp-posts in a certain street.  Tim, who was an early riser, arrived first on the job, and had painted three on the south side when Pat turned up and pointed out that Tim’s contract was for the north side.  So Tim started afresh on the north side and Pat continued on the south.  When Pat had finished his side he went across the street and painted six posts for Tim, and then the job was finished.  As there was an equal number of lamp-posts on each side of the street, the simple question is:  Which man painted the more lamp-posts, and just how many more?