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It was the 15 October 1502, just a few hours before midnight in an old tavern at the docks. Emerald raised two fingers, after repeatedly looking at his three cards, before finally answering the awaiting dealer. "Stick!" His voice was a bit shaky, since his last savings were at stake. As each player started to reveal his cards, Emerald quickly counting their points - and with 28, he was the highest so far. But this just wasn't his lucky day, and just as he revealed his cards, the dealer started to smile - revealing his 31 points.

"I can't believe it! Again!" Emerald dug his nails into his wooden chair, looking up to the dealer. "I don't have more with me. I'll pay the rest next month, alright?"

The dealer nodded, before asking with another smile "Tell ye what... I'll give ya chance ta 'win it back. With a simple lil' bet."

Emerald raised an eyebrow, "A bet?"

The dealer calmly nodded once more while reaching for the other players' cards. "Yeah. Remember that ol' bookworm th'was here earlier?"

Emerald shrugged. "The guy that blabbered about a round world?" he scratched his chin. "What about him?"

The dealer's smile turned into a greedy grin. "Prove me that th'world is a ball, and you get m'winnings. If ya can't, I get double. 'til Friday. Deal?"

Emerald had the luck to talk with the scholar from before and smiled, quickly standing up to shake the dealers hand. "Deal. But I think I can prove it to you tonight, if you still stay sober for another hour or two."

Puzzle

How can Emerald prove that the world is round without leaving the city? And how can he do it in the same night?

For extra fun: What's the game they're playing?

(This is my first riddle here, and I wanted to add a bit of atmosphere to it - but since I'm not a native English speaker, my writing style is probably a bit weird. ;) Still, good luck 'solving' it. It's not too hard. Also, tagging puzzles is a puzzle by itself!)

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    $\begingroup$ The story is delightful, and if I may say, your writing style is excellent. $\endgroup$ – dennisdeems Jul 14 '15 at 14:23
  • $\begingroup$ @dennisdeems Thanks, I wasn't sure how it'ld turn out for others to read ;) Always difficult to judge - at least for me! $\endgroup$ – Katai Jul 14 '15 at 16:01
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On the 15th October 1502

there was a lunar eclipse, with the TD of greatest eclipse at 23:10:40.

As the eclipse progresses, the Moon slowly moves through Earth's shadow.

Every time that shadow is seen, its edge is round. The only solid that always projects a round shadow is a sphere.

For extra fun: The game being played here is

Thirty-One (Credit to @Len)

Reasoning on why it could not also be a disk: Spherical Proof

Catalog of Lunar Eclipses

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    $\begingroup$ @alexmc - "for extra fun", the game sounds like Thirty-one which also has many other names. $\endgroup$ – Len Jul 14 '15 at 15:37
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    $\begingroup$ Thanks @Len! Haha, loving the alternative names for it - I'll have to brush up on my Nickel Nock. $\endgroup$ – alexmc Jul 14 '15 at 16:31
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    $\begingroup$ @Len From reading the rules for 31, it sounds like it was incorrectly played in the riddle... if the dealer had 31 he should have turned it over immediately; otherwise, since he wasn't the lowest value he shouldn't have lost anything. $\endgroup$ – Michael Jul 15 '15 at 3:39
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    $\begingroup$ @Katai they're playing sailor rules. No immediate turnover, so you can still beat the dealer with a player 31, since as a player you can turnover immediately! (But you usually also lose double against a 31 from the dealer if you can't beat it) $\endgroup$ – Falco Jul 15 '15 at 9:09
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    $\begingroup$ @SteveMatthews Its a lunar eclipse. They seldom occur during daytime. $\endgroup$ – Taemyr Jul 15 '15 at 13:34
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alexmc's answer is more robust than this one, but I thought this was also a fun solution to point out. Not as mathematically sound, but also more widely applicable.

Take the barkeep to the nearby ocean. First, take a ruler or something straight, and try to line it up with the horizon. You will be able to see that the horizon is in fact curved, with the edges lower than the middle. Then wait for a ship to either enter into sight or leave. You will notice that the first (or last) thing you see is the mast. This shows that the earth is also curved in that direction. With curvature on two perpendicular axes, you could conclude that the earth, or at least the part you are standing on, is round.

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    $\begingroup$ That was actually the second possibility, yes - and the reason why the tavern was close to the harbor ;D Gj $\endgroup$ – Katai Jul 14 '15 at 21:36
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    $\begingroup$ @Katai Wait, the tavern was close to the harbor solely on the off-chance that somebody would make a bet with someone else that they couldn't prove the world was round? $\endgroup$ – Michael Jul 15 '15 at 3:41
  • $\begingroup$ No--these tests work during the day. The puzzle says this happens at night. $\endgroup$ – Loren Pechtel Jul 15 '15 at 3:59
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    $\begingroup$ @LorenPechtel Actually, it's surprisingly easy to see ships on the horizon at night if you look closely. Outside of a city, at least. I think it's reasonable to assume that in 1502 light pollution isn't a problem. $\endgroup$ – Nic Hartley Jul 15 '15 at 6:44
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    $\begingroup$ @Michael Nono, what I meant was that the tavern is at a harbor, to allow for someone to bring the "sinking ship" solution as alternative to the lunar eclipse ;) - but that location was chosen with "out of world" (my) reasoning, not because anyone building the tavern thought "Hey, they could bet about round worlds in 20 years!". $\endgroup$ – Katai Jul 15 '15 at 7:42

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