$184,467,440,737,095,516.15
Over $184 Quadrillion
If anyone wants an explanation - please ask.
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The first time I have seen this, the winner of a game of chess put a grain of rice on the first square and asked his opponent to double the number on each square, with the final number of grains as his prize.
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I think your initial quotation paints a neat picture of the value of $1.84 x 10^17
or even a Quadrillion 
Probably “a ton of rice”
At least more than the total harvest of the country the game was played.
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I thought this was an interesting teaser and I learned something new from your solution.
I rather liked the title, though it has prompted a follow-up teaser:
Why would it be most unlikely to see such a crescent given: “The sky at night, with the moon shining bright.”
And what would be an accurate description if one looked up at the sky and saw such a crescent?
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Hi Ravvie, nice teaser !!
Well (approximately) … (and with tongue in cheek)
The moon doesn’t emit light, it reflects light originating from the sun. Perhaps I should have started with " … the moon reflecting light"
The waning crescent, coloured yellow in the diagram, should only occupy the left-hand side of the diagram, ie there should be no yellow moon to the right of EH. The earth shadow should be slightly bigger than the moon.
The Crescent moon should appear rotated anti-clockwise by about 25 deg when seen from where I live.
The colouring and shading probably wasn’t quite …
Probably best if I stop there, because i’ve got a night flying training sortie starting at 18:00 and my student has just arrived
PS: i’m not sure if any of my comments are correct, I’ll look more carefully this next month or so
I realised when drafting the teaser variation that it was open to a range of answers and you haven’t disappointed!
This is a key observation. However, the dark side is not caused by the Earth’s shadow. It is simply night time on the moon. The edge of the dark area is dusk or dawn on the moon and is called the terminator in astronomy. It passes through ECH and although is a great circle on the moon, what we see of ECH from Earth is a semi-ellipse, it is not circular. Of course, such nuances would mess up the original teaser!
You are right that the orientation of the crescent varies by location. When I was in Peru last year, the crescent Moon was U shaped rather than C shaped (loosely speaking!)
Apart from what causes the dark area, I agree with your observations though some I hadn’t thought of.
There’s still the second part to answer…
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Hi Ravvie, I think you are going to have to outline the thinking behind the second part of your teaser !
The image is consistent with an annular eclipse of the sun. This is similar to a total eclipse where the moon fully obscures the sun. Annular eclipses occur when the moon is slightly further away from the Earth than normal (or the Earth is closer to the sun than normal), so the moon’s disc appears too small to cover the whole sun. This is because orbits are slightly elliptical.
The image would be either second or third contact, being the start or end of the annular eclipse. Between those two it is sometimes described as a “ring of fire”. I haven’t witnessed one, it’s on my list, but we did go to France to see the total eclipse in 1999. Highly recommended.
This would suggest an alternative title: “The daytime sky, with the sun shining dimly”. I prefer the original though!
Bit of tidying up this morning. Removed the three volumes of Lord of the Rings to dust them off. Reminded me of this little teaser
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Hi Don,
the answer in centimeters features two digits from the number of your post.
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Hi Mulberry, I think you could be correct.
But I need to check a bit more carefully, because the puzzle was set up in those old-fashioned inches …
Mrs R came up with an answer that I think is consistent with @Mulberry’s cryptic answer.
But I have a very different answer!
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Too easy to answer, there can only be one answer not two.
Would you like me to message the answer to you? And then wait two days and post here too?
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I think it’s the same as the volume number on one of the books.
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Hi WalnutTree,
I’m sure that all who have posted so far, have the same answer as Mrs R, and that includes myself and, based on the wording of your post, I imagine your good-self too.
Ravvie, on the other hand, often comes along with some (outrageous ) alternative solution, which would baffle even BAM, if he were still around. They certainly baffle me, I await with trepidation !
Let’s hold out until tomorrow, then we can each reveal our logic …
This does no longer surprise me Ravvie
Nothing too surprising this time.
I think I have the same answer as @WalnutTree and @SteveD
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