Ladies' Diary/Money Counting Problem

Puzzle

In how long a time would a million of millions of money be in counting,

supposing one hundred pounds to be counted every minute without intermission,

and the year to consist of $365$ days, $5$ hours, $45$ minutes?

Solution

The number of minutes $m$ in the year is calculated as:

\(\ds m\)

\(=\)

\(\ds \paren {365 \times 24 \times 60} + \paren {5 \times 60} + 45\)

\(\ds \)

\(=\)

\(\ds 525 \, 600 + 300 + 45\)

\(\ds \)

\(=\)

\(\ds 525 \, 945\)

The number of $100$s $h$ in a million of millions is calculated as:

\(\ds h\)

\(=\)

\(\ds \dfrac {1 \, 000 \, 000 \times 1 \, 000 \, 000} {100}\)

\(\ds \)

\(=\)

\(\ds 10 \, 000 \, 000 \, 000\)

This gives the total number of minutes to count the money.

The total number of years $t$ needed to count the money is therefore:

\(\ds t\)

\(=\)

\(\ds \dfrac {10 \, 000 \, 000 \, 000} {525 \, 945}\)

\(\ds \)

\(=\)

\(\ds 19013 \text { years}, 207 \, 715 \text { minutes}\)

\(\ds \)

\(=\)

\(\ds 19013 \text { years}, 3461 \text { hours}, 55 \text { minutes}\)

\(\ds \)

\(=\)

\(\ds 19013 \text { years}, 144 \text { days}, 5 \text { hours}, 55 \text { minutes}\)

$\blacksquare$

Historical Note

This was the first mathematical question to be published in The Ladies' Diary.

It was posed in the year $1707$.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The Ladies' Diary or Woman's Almanac, $\text {1704}$ – $\text {1841}$: $136$