Another maths curiosity from the Futility Closet:

Fortuitous numbers
In American usage, 84,672 is said EIGHTY FOUR THOUSAND SIX HUNDRED SEVENTY TWO. Count the letters in each of those words, multiply the counts, and you get 6 × 4 × 8 × 3 × 7 × 7 × 3 = 84,672.

Here’s something I’ve (pointlessly) struggled with for a long time, now. Can you complete this sentence?

Written as words, there are _____________ letters in this sentence.

Use Excel’s LEN() function and AutoSum and try it like this, writing it out one word at a time.

So, forty three letters so far, with those two empty boxes. If you were to write forty three into those boxes, the total would obviously be more than forty three. A little trial-and-error, and we get

the answer fifty three. Well, that was fairly straightforward. Let’s try a slightly different sentence.

Maybe this isn’t so difficult, after all. One more?

That’s not right, there are forty nine letters in that sentence, not forty eight.

But now there are forty eight. Is it not possible to accurately complete that sentence, then?