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  • You are the cargo director on the maiden voyage of the S.S. Buoyant,

  • and you've agreed to transport several tanks containing

  • the last specimens of a critically endangered fish species

  • to their new aquarium.

  • Unfortunately, as you're passing through shark-infested waters,

  • the boat is battered by a fierce storm, throwing your precious cargo overboard.

  • And to make matters worse,

  • no one seems certain just how many fish tanks are missing.

  • Fortunately, you have a rescue sub at your disposal,

  • but only enough fuel for one trip to the ocean floor.

  • You need to know where the tanks are

  • so you can gather them all in one quick pass.

  • Not a single fish can be lost.

  • You decide to scan the three sectors of the ocean floor

  • where the cargo could have landed.

  • Thermal imaging shows 50 organisms in the area,

  • and you quickly realize that that number includes both your fish

  • and some ravenous sharks.

  • You flip on the sonar to get a better look.

  • The image for Sector Alpha shows four tanks and two sharks,

  • the image for Sector Beta shows two tanks and four sharks,

  • and the image for Sector Gamma is blank.

  • Your sonar has malfunctioned,

  • and you're going to have to go with the info you have.

  • You check the shipping notes,

  • but all you learn is that each tank had the same number of fish inside.

  • The cargo hold had space for anywhere from 1 to 13 total tanks.

  • And finally, the old captain tells you that this area has the odd property

  • that no two sectors can have the same number of sharks,

  • but every sector will have at least one,

  • and no more than seven.

  • There's no time to waste.

  • The tanks won't withstand the pressure much longer.

  • As you descend in the sub, you review everything you know.

  • How many fish tanks do you need to find in Sector Gamma?

  • Hurry, the fate of an entire species depends on you.

  • Pause here if you want to figure it out for yourself.

  • Answer in: 3

  • Answer in: 2

  • Answer in: 1

  • At first, it seems like there are just too many missing pieces of information.

  • After all, you don't know how many fish or how many tanks there are,

  • let alone how many fish are in each one.

  • But then you remember the best way

  • to compare multiple pieces of partial information - a table.

  • Since we know there are thirteen tanks at most,

  • and we already see six tanks in Sectors Alpha and Beta,

  • we know the total number of tanks must be between 6 and 13.

  • We also know that each sector has a different amount of sharks

  • with no more than seven in each one.

  • Since there are two in Sector Alpha and four in Sector Beta,

  • Sector Gamma can have 1, 3, 5, 6, or 7 sharks.

  • What about the number of endangered fish?

  • Out of the 50 total organisms in all three sectors,

  • we know at least seven are sharks,

  • leaving a maximum of 43 fish inside all the tanks.

  • And the more sharks we find in Sector 3, the fewer fish there are to save.

  • Now, remember that the fish are equally distributed across all the tanks.

  • Why is that important?

  • Because it means that one of the possible values for the total amount of fish

  • must be divisible by one of the possible values for the total amount of tanks.

  • And looking at the table, we can see that the only combination that works

  • is 39 fish divided between 13 tanks with three fish in each.

  • With sharks swarming around,

  • you quickly pilot the sub through the first two sectors

  • before retrieving the remaining seven tanks in Sector Gamma.

  • You've saved the species and taken an impromptu dive.

  • All in all, not a bad day, unless you happen to be a hungry shark.

You are the cargo director on the maiden voyage of the S.S. Buoyant,

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【TED-Ed】Can you solve the fish riddle? - Steve Wyborney

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    小爸   に公開 2017 年 07 月 02 日
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