Puzzles
8! minutes
How many weeks are there in 8! (\(8\times 7\times 6\times 5\times 4\times 3\times 2\times 1\)) minutes?
Show answer & extension
Hide answer & extension
$$8\times 7\times 6\times 5\times 4\times 3\times 2\times 1 \mbox{ minutes}$$
$$= 8\times 7\times 4\times 3\times 1 \mbox{ hours}$$
$$= 7\times 4\times 1 \mbox{ days}$$
$$= 4\times 1 \mbox{ weeks}$$
$$= 4 \mbox{ weeks}$$
Extension
8 is the smallest number \(n\) such that \(n!\) minutes is a whole number of weeks.
What is the smallest number \(m\) such that \(m!\) seconds is a whole number of weeks?
