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.