# Enigmatic Code

Programming Enigma Puzzles

## Puzzle #21: Six weeks of seconds

From New Scientist #3247, 14th September 2019 [link]

Which number is bigger:

The product of all the whole numbers from 1 to 10 inclusively, sometimes written as 10 factorial or 10!

or:

The number of seconds in six weeks?

Can you work it out without resorting to a calculator?

[puzzle#21]

### One response to “Puzzle #21: Six weeks of seconds”

1. Jim Randell 14 September 2019 at 8:07 am

Solution: Neither is bigger – both numbers have the same value.

Both numbers are equal to 3,628,800, but we don’t need to work out the values of the numbers.

We can write 6 weeks as:

6 weeks =
(6 × 7) days =
(6 × 7 × 24) hours =
(6 × 7 × 24 × 60) minutes =
(6 × 7 × 24 × 60 × 60) seconds =
(6 × 7 × 24 × 3600) seconds =
(6 × 7 × 24 × (36 × 100)) seconds =
(6 × 7 × (3 × 8) × ((4 × 9) × (2 × 5 × 10)) seconds =
(2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10) seconds =
factorial(10) seconds

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