Can you solve the fish riddle? –  Steve Wyborney

Can you solve the fish riddle? – Steve Wyborney

August 6, 2019 100 By William Morgan

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.