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.