THE CONVERTED MISER.
(
Money Puzzles)
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.
Answer:
As we are not told in what year Mr. Jasper Bullyon made the generous
distribution of his accumulated wealth, but are required to find the
lowest possible amount of money, it is clear that we must look for a
year of the most favourable form.
There are four cases to be considered--an ordinary year with fifty-two
Sundays and with fifty-three Sundays, and a leap-year with fifty-two and
fifty-three Sundays respectively. Here are the lowest possible amounts
in each case:--
313 weekdays, 52 Sundays L112,055
312 weekdays, 53 Sundays 19,345
314 weekdays, 52 Sundays No solution possible.
313 weekdays, 53 Sundays L69,174
The lowest possible amount, and therefore the correct answer, is
L19,345, distributed in an ordinary year that began on a Sunday. The
last year of this kind was 1911. He would have paid L53 on every day of
the year, or L62 on every weekday, with L1 left over, as required, in
the latter event.
