112.—­A PUZZLING LEGACY.

A man left a hundred acres of land to be divided among his three sons—­Alfred, Benjamin, and Charles—­in the proportion of one-third, one-fourth, and one-fifth respectively.  But Charles died.  How was the land to be divided fairly between Alfred and Benjamin?

113.—­THE TORN NUMBER.

[Illustration]

I had the other day in my possession a label bearing the number 3 0 2 5 in large figures.  This got accidentally torn in half, so that 3 0 was on one piece and 2 5 on the other, as shown on the illustration.  On looking at these pieces I began to make a calculation, scarcely conscious of what I was doing, when I discovered this little peculiarity.  If we add the 3 0 and the 2 5 together and square the sum we get as the result the complete original number on the label!  Thus, 30 added to 25 is 55, and 55 multiplied by 55 is 3025.  Curious, is it not?  Now, the puzzle is to find another number, composed of four figures, all different, which may be divided in the middle and produce the same result.

114.—­CURIOUS NUMBERS.

The number 48 has this peculiarity, that if you add 1 to it the result is a square number (49, the square of 7), and if you add 1 to its half, you also get a square number (25, the square of 5).  Now, there is no limit to the numbers that have this peculiarity, and it is an interesting puzzle to find three more of them—­the smallest possible numbers.  What are they?

115.—­A PRINTER’S ERROR.

In a certain article a printer had to set up the figures 5^4x2^3, which, of course, means that the fourth power of 5 (625) is to be multiplied by the cube of 2 (8), the product of which is 5,000.  But he printed 5^4x2^3 as 5 4 2 3, which is not correct.  Can you place four digits in the manner shown, so that it will be equally correct if the printer sets it up aright or makes the same blunder?

116.—­THE CONVERTED MISER.

Mr. Jasper Bullyon was one of the very few misers who have ever been converted to a sense of their duty towards their less fortunate fellow-men.  One eventful night he counted out his accumulated wealth, and resolved to distribute it amongst the deserving poor.

He found that if he gave away the same number of pounds every day in the year, he could exactly spread it over a twelvemonth without there being anything left over; but if he rested on the Sundays, and only gave away a fixed number of pounds every weekday, there would be one sovereign left over on New Year’s Eve.  Now, putting it at the lowest possible, what was the exact number of pounds that he had to distribute?

Could any question be simpler?  A sum of pounds divided by one number of days leaves no remainder, but divided by another number of days leaves a sovereign over.  That is all; and yet, when you come to tackle this little question, you will be surprised that it can become so puzzling.

117.—­A FENCE PROBLEM.