Romancing the numbers

A favorite book of mine is Edward MacNeil's Mathsemantics (available for under a fiver at Amazon: http://url.ie/gzul).  It's about how even math-savvy people's math skills go pear-shaped when problems aren't presented on squared paper: they can do 5 + 3 no problem but go south when the task is 5 oranges + 3 apples.  If that makes you go "Wha'?", then  go read the book.  MacNeil is big on getting his employees to guesstimate numbers: leveraging the (perhaps few) facts that are available to come up with something that can turn an honest profit by being more accurate or more reliable than the competition.  A couple of anecdotes suggest that he won't leave that sort of thing in the office but does a bit of Socratic method round the dinner table.  I guess the kids enjoy it if they've grown up with it - but I wouldn't be totally surprised if they run out of the room screaming (and hungry) when he enjoins them to guess the number of rice grains on his plate.  That's a bit of a long preamble to a question that No.2 Daughter asked in the car a few months ago:

"How many people make a proposal of marriage in/on the Eiffel Tower every day?"

Being in the car meant that we couldn't google up the answer and even if you have google AND WolframAlpha at hand, it's not straightforward.  I'll let you give the conundrum a whirl yourself.


Here's enough relevant information: wikipedia asserts that in 2006 6,712,200 people passed through the Eiffel turnstile; OTOH, the CSO says that in the same year 22,089 marriages occurred in Ireland - that's 5.2 per 1000 head.  I'm assuming that marriages are always preceded by a proposal and that the rate has reached a steady state - so the rate of engagements/proposals is the same but they occur a few months earlier.  The rate sounds sensible in an order of magnitude (OoM) sort of way - it takes two to tango, you get married once (some more often, some not at all) and you live for 100 years gives you an annual rate of 1000 people / 100 years = 10 people per 1000 start married life each year.

Of the 6.7M people who went up La Tour in 2006, there were (5.2/1000) * 6.7M marriages that year and an equal number of engagements.  That's 35,000 or about 100 a day!  Having done the math to get the right OoM, you should adjust to take into account the iconic nature of La Tour in the world's most romantic city.  The 6.7M people who go up are not a random selection of people accosted in the Metro or selected from the phone books in France.  So I'll double the number and put folding money on being right(ish).  I'm still amazed, though.