Can you solve the secret werewolf riddle? - Dan Finkel
You’re on the trail of a werewolf
that’s been terrorizing your town.
After months of detective work,
you’ve narrowed your suspects to
one of five people:
the mayor,
the tailor,
the baker,
the grocer,
or the carpenter.
You’ve invited them to dinner
with a simple plan:
you’ll slip a square of
a rare werewolf antidote
into each of their dinners.
Unfortunately, your pet goat
just ate four of the squares,
and you only have one left.
Luckily, the remaining square is 50 grams,
and the minimum effective dose
is 10 grams.
If you can precisely divide the
square into fifths
you’ll have just enough
antidote for everyone.
You’ll have to use a laser-cutting tool
to cut up the square;
every other means available to you
isn’t precise enough.
There are 8 points that can act
as starting or ending points for each cut.
To use the device, you’ll
have to input pairs of points
that tell the laser where to begin
and end each cut,
and then the laser executes
all the cuts simultaneously.
It’s okay to cut the square
into as many pieces as you want,
as long as you can group them
into 10 gram portions.
But you can’t fold the square
or alter it otherwise,
and you only get one shot
at using the laser cutter.
The full moon is rising,
and in a moment someone
will transform and tear you all apart
unless you can cure them first.
How can you divide the antidote
into perfect fifths,
cure the secret werewolf,
and save everyone?
Pause the video now if you want
to figure it out for yourself.
Answer in 3
Answer in 2
Answer in 1
When it comes to puzzles that
involve cutting and rearranging,
it’s often helpful to actually
take a piece of paper
and try cutting it up to see what
you can get.
If we cut BF and DH we’d get fourths,
but we need fifths.
Maybe there’s a way to shave a bit off
of a quarter to get exactly one fifth.
Cutting BE looks good at first,
but that last cut
takes a off a quarter of a quarter,
leaving us with a portion of 3/16:
just smaller than a fifth,
and not enough to cure a werewolf.
What if we started with BE instead?
That would also give us a quarter.
And is there a way to shave
just a bit more off?
Both DG and CH look promising.
If we make one more cut, from A to F,
we may start to notice something.
With these four cuts—from B to E,
D to G, F to A,
and H to C—we’ve got four triangles
and a square in the middle.
But the pieces that make
each triangle can also be
rearranged to make a square
identical to the middle one.
This means that we’ve split
the antidote into perfect fifths!
What’s interesting about this
sort of problem
is that while it’s possible to solve
it by starting from the geometry,
it’s actually easier to start
experimenting and see where that gets you.
That wouldn’t be as viable if the square
had, say, 24 cut points,
but with just 8 there
are only so many reasonable options.
You secretly dose each of the townspeople
as the full moon emerges in the sky.
And just as you do,
a terrible transformation begins.
Then, just as suddenly, it reverses.
Your measurements were perfect,
and the people and animals of the
town can rest a little easier.
