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.