Can you solve the passcode riddle? - Ganesh Pai

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In a dystopian world, your resistance group is humanity’s last hope. Unfortunately, you’ve all been captured by the tyrannical rulers and brought to the ancient coliseum for their deadly entertainment. Will you be able to solve the passcode riddle and get everyone out safely? Ganesh Pai shows how.

Lesson by Ganesh Pai, animation by Jun Zee Myers.

In this dystopian world, your resistance
group is humanity's last hope.

Unfortunately, you've all been captured
by the tyrannical rulers

and brought to the ancient colosseum
for their deadly entertainment.

Before you're thrown into the dungeon,

you see many numbered hallways
leading outside.

But each exit is blocked by
an electric barrier

with a combination keypad.

You learn that one of you will be allowed
to try to escape by passing a challenge

while everyone else will be fed to
the mutant salamanders the next morning.

With her perfect logical reasoning,
Zara is the obvious choice.

You hand her a concealed audio transmitter
so that the rest of you can listen along.

As Zara is led away,

you hear her footsteps echo
through one of the hallways,

then stop.

A voice announces
that she must enter a code

consisting of three positive whole numbers
in ascending order,

so the second number is greater than
or equal to the first,

and the third is greater than
or equal to the second.

She may ask for up to three clues,

but if she makes a wrong guess,

or says anything else,

she'll be thrown back into the dungeon.

For the first clue, the voice says
the product of the three numbers is 36.

When Zara asks for the second clue,

it tells her the sum of the numbers

is the same as the number
of the hallway she entered.

There's a long silence.

You're sure Zara remembers
the hallway number,

but there's no way for you to know it,

and she can't say it outloud.

If Zara could enter the passcode
at this point, she would,

but instead, she asks for the third clue,

and the voice announces that the largest
number appears only once

in the combination.

Moments later, the buzz of the electric
barrier stops for a few seconds,

and you realize that Zara has escaped.

Unfortunately, her transmitter
is no longer in range,

so that's all the information you get.

Can you find the solution?

Pause on the next screen
to work out the solution.

3

2

1

You're worried about the fact that you
don't know Zara's hallway number,

but you decide to start
from the beginning anyways.

From the first clue, you work out all of
the eight possible combinations

that come out to a product of 36.

One of these must be right,
but which one?

Now comes the hard part.

Even though you don't know which number
you're looking for,

you decide to work out the sum
of each combination's three numbers.

That's when it hits you.

All but two of the sums are unique,

and if the hallway number had matched
any of these,

Zara would have known the correct
combination right then and there

without asking for the third clue.

Since she did ask for the clue,

the hallway number must have
matched the only sum

that appears more than once in the list:

thirteen.

But which of the two combinations
that add up to thirteen is correct:

1,6,6,

or 2,2,9?

That's where the third clue comes in.

Since it tells us that the largest
number must be unique,

2,2,9 must be the code.

When night falls, you and the others
escape through hallway thirteen

and rejoin Zara outside.

You've freed yourselves through
math and logic.

Now it's time to free
the rest of the world.