(related to Problem: The Converted Miser)
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 favorable 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 — £$112,055$ * $312$ weekdays, $53$ Sundays — £$19,345$ * $314$ weekdays, $52$ Sundays — no solution possible. * $313$ weekdays, $53$ Sundays — £$69,174$
The lowest possible amount, and therefore the correct answer, is £19,345, distributed in an ordinary year that began on a Sunday. The last year of this kind was $1911.$ He would have paid £$53$ on every day of the year, or £$62$ on every weekday, with £$1$ left over, as required, in the latter event.
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