Name: Can you solve the stolen rubies riddle? - Dennis Shasha
Uploaded: 2020-02-05T02:34:30.000Z
Duration: 4 min 51 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

One of the kingdom's most prosperous merchants

Advanced passive voice

has been exposed for his corrupt dealings.

But the scoundrel and his allies at court

which portion of the rubies  were bought with ill-gotten wealth,

the fine will be determined through  a game of wits between the merchant

and the king's most clever advisor – you.

The merchant will be allowed to discreetly divide his rubies

among three boxes, which will then be placed in front of you.

and must write a number  between 1 and 30 on each,

before putting a card in front of each of the boxes.

as many rubies as the number written on the corresponding card,

But if your number is greater than  the number of rubies actually there,

the scoundrel gets to keep the entire box.

The king puts just two constraints on how the scoundrel distributes his rubies.

Each box must contain at least two rubies

and one of the boxes must contain  exactly six more rubies than another—

but you won't know which boxes those are.

the merchant hides the gems,  and the boxes are brought in front of you.

in order to guarantee the largest possible fine for the scoundrel

and the greatest compensation  for his victims?

Pause the video now if you want to figure it out for yourself.

You don't want to overshoot by being too greedy.

to get more than half of the scoundrel's  stash.

The situation resembles an  adversarial game like chess –

only here you can't see the  opponent's position.

To figure out the minimum number of rubies you're guaranteed to win,

you need to look for the worst case scenario,

as if the merchant already knew your move

and could arrange the rubies  to minimize your winnings.

Because you have no way of knowing which boxes will have more or fewer rubies,

you should pick the same number for each.

The scoundrel might have allocated the rubies as 8, 14 and 8.

In that case, you'd receive 9 from the middle box and no others.

On the other hand, you can be sure that at least two boxes

Those could not be the two that  differ by 6,

because every box must have  at least 2 rubies.

In that case, the third box would have at most 13 rubies—that's 7 plus 6.

You now know, by what's called a proof by contradiction,

that two of the boxes have  8 or more rubies.

as you can see by thinking again about the 8, 14, 8 scenario.

You've recovered more than half the  scoundrel's fortune

And though he's managed to hold on to some of his rubies,

his fortune has definitely  lost some of its shine.

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Can you solve the stolen rubies riddle? - Dennis Shasha

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