Can you solve the dragon jousting riddle? - Alex Gendler
After centuries of war,
the world’s kingdoms
have come to an agreement.
Every five years, teams representing
the elves, goblins, and treefolk
will compete in a grand tournament
of dragon jousting.
Every team will face
each of the others once.
The kingdom whose team wins the most
matches will rule all of Center-Realm
until the next tournament.
To prevent any outside meddling,
the games are to be conducted
in absolute secret
except for a group of wizards
who will make sure
nobody uses enchantments, hexes,
or spells to cheat.
You’ve been given the extremely
important job of recording the scores
for the first inaugural tournament.
But the opening celebrations
get a bit out of control,
and when you wake up,
you realize the games
are already underway.
Fortunately, no one has noticed
your absence so far.
However, you need to get up to speed
quickly;
if your boss,
the head tournament official,
finds out you’ve been sleeping on the job,
you’ll lose your head.
After weighing your options,
you decide to offer your life’s savings
to one of the regulation wizards
in return for the information,
giving him your blank scorecard
to fill out.
But before he can finish,
your boss walks into the tent.
You barely manage to hide the scorecard
in time,
and the wizard excuses himself.
Your boss chuckles.
“Hope you didn’t believe anything
Gorbak’s been saying—
he’s been cursed to tell only lies,
even in writing.
Anyway, can you believe how low-scoring
the tournament’s been?
Every team has played at least once,
yet not a single match with
a combined score of more than five hits!
Anyhow, I’ll be back in a minute
to review your scorecard.”
You laugh along,
and when he leaves you look
at the partially completed card,
now knowing every single number
on it is wrong.
You’ve only got one chance
to save yourself,
so what’s the real score of each match?
Pause now to figure it out for yourself.
The incredible thing about this riddle
is that you can reach the solution
despite an almost complete lack
of correct information.
And that’s possible because
knowing that something is false
is meaningful information
in its own right.
The first key is to realize that no team
will play more than two matches,
since there are only two other teams.
So if the elves didn’t actually play
one match,
and the goblins didn’t actually play two,
the truth must be that elves played two
and goblins played one.
For the elves to have played two matches,
they must’ve faced each of the other teams
once.
And since goblins have only played
one match so far— against the elves—
that means the match between goblins
and treefolk has not occurred yet.
We know it’s false that the treefolk tied
zero matches,
which means their bout
against the elves must’ve tied.
We also know that the elves won
at least one match,
and since they tied against the treefolk,
they must have beaten the goblins.
But can we figure out the actual scores?
Let’s start with the elf-treefolk tie.
Because no more than five total hits
were scored,
the final tally must’ve been
0-0, 1-1, or 2-2.
But the treefolk must’ve scored
some hits,
and it’s false that they only had one hit
scored against them.
The only option that leaves is 2-2.
In the match between elves and goblins,
the goblins must’ve scored
at least one hit.
And the elf score must be 2 or more
for them to have won the match.
This leaves only a few possibilities
that add up to 5 or less.
The elves couldn’t have scored three,
so that eliminates these two.
And their total hits scored
across both matches can’t add up to six,
so this one’s out too.
So the score must’ve been 2-1.
With one match remaining,
you’ve managed to save your job—
and your neck.
Gorbak the wizard may have lied,
but your deductive skills
quickly evened the score.
