After many years of fighting, the kingdoms of the world have finally agreed to settle their differences in a unique way. Every five years, teams from the elves, goblins, and treefolk compete in a grand tournament of dragon jousting. Each team plays against every other team once, and the team with the most wins gets to rule all of Center-Realm until the next tournament. To keep things fair, a group of wizards watches over the games to make sure no one cheats using magic.
You have an important job: recording the scores of the first tournament. But after a night of wild celebrations, you wake up to find the games have already started! Luckily, no one has noticed your absence yet, but you need to catch up fast. If your boss, the head tournament official, finds out you’ve been slacking, you could be in big trouble.
Desperate for help, you offer your life savings to one of the wizards to fill out your blank scorecard. Just as he starts, your boss walks in. You quickly hide the scorecard, and the wizard leaves. Your boss laughs and says, “I hope you didn’t believe anything Gorbak has been saying—he’s cursed to tell only lies, even in writing. Anyway, can you believe how low-scoring the tournament has been? Every team has played at least once, yet not a single match has had a combined score of more than five hits! I’ll be back in a minute to review your scorecard.”
Once he leaves, you realize that every number on the scorecard is wrong. You have one chance to figure out the real scores and save your job. What do you do?
Even with little correct information, you can solve this puzzle. First, understand that each team plays only two matches because there are only two other teams. If the elves didn’t play one match and the goblins didn’t play two, then the truth must be that the elves played two matches and the goblins played one.
For the elves to have played two matches, they must have faced both the goblins and the treefolk. Since the goblins have only played one match so far—against the elves—it means the goblins and treefolk haven’t played yet. We know it’s false that the treefolk tied zero matches, so their match against the elves must have ended in a tie. We also know the elves won at least one match, so they must have beaten the goblins.
Now, let’s figure out the scores. In the elf-treefolk tie, since no match had more than five total hits, the score could be 0-0, 1-1, or 2-2. The treefolk must have scored some hits, and it’s false that they only had one hit scored against them. The only option left is 2-2.
In the match between elves and goblins, the goblins must have scored at least one hit, and the elves must have scored 2 or more to win. The scores must add up to 5 or less. The elves couldn’t have scored three, so that eliminates those options. Their total hits across both matches can’t add up to six, so that option is out too. Therefore, the score must have been 2-1.
With one match left to play, you’ve managed to save your job—and your neck. Gorbak the wizard may have lied, but your clever thinking helped you figure out the real scores!
Imagine you are part of the dragon jousting tournament. Create a short skit with your classmates where each of you plays a role: an elf, a goblin, a treefolk, or a wizard. Act out a scene where you discuss strategies and the importance of fair play. This will help you understand the dynamics between the teams and the role of the wizards in ensuring fairness.
Recreate the scorecard puzzle from the article. Use a blank scorecard and try to fill in the scores based on the clues provided. Work in pairs to solve the puzzle, discussing your reasoning with your partner. This will help you practice logical thinking and problem-solving skills.
Using the information from the article, calculate the possible scores for each match. Create a chart showing all possible outcomes and discuss why certain scores are not possible. This activity will reinforce your understanding of mathematical constraints and logical deduction.
Write a short story from the perspective of one of the teams or the wizard Gorbak. Describe the events of the tournament and how they felt about the outcome. This will help you explore character perspectives and enhance your creative writing skills.
Hold a class debate on the importance of fair play in competitions. Discuss the role of the wizards in the tournament and whether their presence is necessary. This will encourage you to think critically about ethics in sports and the importance of honesty.
After centuries of conflict, the kingdoms of the world have reached an agreement. Every five years, teams representing the elves, goblins, and treefolk will compete in a grand tournament of dragon jousting. Each team will face every other team once, and the kingdom whose team wins the most matches will rule all of Center-Realm until the next tournament. To prevent any outside interference, the games will be conducted in complete secrecy, except for a group of wizards who will ensure that no one uses enchantments or spells to cheat.
You have been assigned the important task of recording the scores for the inaugural tournament. However, the opening celebrations get a bit out of hand, and when you wake up, the games are already in progress. Fortunately, no one has noticed your absence so far. However, you need to catch up quickly; if your boss, the head tournament official, finds out you’ve been sleeping on the job, you could be in serious trouble.
After considering your options, you decide to offer your life savings to one of the regulation wizards in exchange for information, giving him your blank scorecard to fill out. But before he can finish, your boss walks into the tent. You manage to hide the scorecard just in time, and the wizard excuses himself. Your boss chuckles, “I hope you didn’t believe anything Gorbak has been saying—he’s been cursed to tell only lies, even in writing. Anyway, can you believe how low-scoring the tournament has been? Every team has played at least once, yet not a single match has had a combined score of more than five hits! I’ll be back in a minute to review your scorecard.”
You laugh along, but once he leaves, you look at the partially completed card, now knowing that every single number on it is incorrect. You have one chance to save yourself, so what’s the real score of each match?
The interesting aspect of this puzzle is that you can arrive at the solution despite having very little correct information. The first key is to realize that no team will play more than two matches since there are only two other teams. If the elves didn’t actually play one match, and the goblins didn’t actually play two, then the truth must be that the elves played two matches and the goblins played one.
For the elves to have played two matches, they must have faced each of the other teams once. Since the goblins have only played one match so far—against the elves—it means the match between the 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 have resulted in a tie. 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 determine the actual scores? Let’s start with the elf-treefolk tie. Since no more than five total hits were scored, the final tally must have been 0-0, 1-1, or 2-2. However, the treefolk must have scored some hits, and it’s false that they only had one hit scored against them. The only option left is 2-2.
In the match between elves and goblins, the goblins must have 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 those options. Their total hits scored across both matches can’t add up to six, so that option is out too. Therefore, the score must have 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.
Tournament – A series of contests between a number of competitors, who compete for an overall prize. – The math tournament challenged students to solve complex problems in a limited time.
Scores – The number of points achieved in a game or test. – After the math quiz, the teacher announced the scores to the class.
Matches – Competitions or contests between two or more parties. – The chess club held several matches to determine the best player.
Goblins – Imaginary creatures often used in stories or games, typically mischievous or evil. – In the logic puzzle, students had to figure out how many goblins were hiding in the cave.
Elves – Mythical beings often depicted as small and magical, usually helpful or mischievous. – The math story problem involved elves who were busy making toys in a workshop.
Treefolk – Fictional creatures resembling trees, often found in fantasy stories. – The treefolk in the story helped the students understand the concept of branching in decision trees.
Puzzle – A game or problem designed to test ingenuity or knowledge. – Solving the math puzzle required careful thinking and attention to detail.
Thinking – The process of considering or reasoning about something. – Critical thinking is essential when solving complex math problems.
Hits – Successful attempts or actions, often used in the context of achieving a goal. – Each correct answer in the math game counted as a hit towards the final score.
Scorecard – A record of scores or points in a game or competition. – The teacher used a scorecard to keep track of each team’s progress during the math challenge.
