Welcome to the annual Sly Wizard Tournament! This exciting event brings together the best wizards from three magical schools to compete in a series of challenges. Your job is to organize the tournament, decide how many events there will be, and set up the scoring system. The wizards will then enter your maze and compete in secret, with only you knowing the results.
The competition kicks off, but there’s a problem. A dark wizard appears and casts a forgetting curse on you, leaving you with no memory of what happened. The three wizards are all convinced they won, but you can’t remember who the real winner is. You need to figure this out quickly to avoid chaos in the wizarding world.
Here’s what you remember: there were at least three events, and each event had a single winner and loser. The scoring system was the same for all events, with first place getting more points than second, and second more than third. All points were positive whole numbers. You also have a scorecard with some notes: in the event called Calchemy, Newt-niz won, Leib-ton came second, and Magnificent Marigold’s Magical Macademy got third. The final scores were 22 points for one school and 9 points for the other two.
To solve the mystery, let’s look at the total scores. The sum of all points in the tournament must be a multiple of the total points from one event. If there were three events with scores of 3, 2, 1, the total would be 18 points (3 events times 6 points). Our total is 40 points.
We can make a table of possibilities: one event totaling 40 points, two totaling 20, four totaling 10, and so on. Since there were at least three events, we can eliminate some options. We also know the smallest possible total for an event is 6 points (3 + 2 + 1), so we can remove options with fewer points. This leaves us with a few possibilities.
If first place received 7 points, the teams with 9 points couldn’t have won an event because their total would be 10 or more. The team with 22 points would have to win all four events, but their total would be 28, which doesn’t work. So, we eliminate that option.
If first place got 5 points, the highest possible score with four events would be 20, which doesn’t match our scores. That leaves us with one possibility: five events each scored 5, 2, 1. The only way to reach 22 points is if the winner finished first four times and second once. The scores of 9 mean one team won once and lost four times, and the other lost once and took second four times.
Based on your notes, Marigold’s Macademy got third place only once in Calchemy. Leib-ton’s second place in Calchemy means they scored 22 points and won the Sly Wizard Tournament. You’ve solved the mystery, saved the day, and prevented a wizarding war. Great job!
Design a magical maze with at least three events. Decide on the scoring system and create a storyline for the maze. Share your maze with classmates and see if they can solve it!
In groups, take on the roles of the wizards and the organizer. Reenact the tournament, using clues and logic to determine the winner. Discuss how different scoring systems could change the outcome.
Work in pairs to create different scoring systems for the tournament. Calculate how these systems would affect the final scores and discuss which system is the fairest.
Write your own short story about a magical tournament with a mystery to solve. Include clues and a logical solution. Share your story with the class and see if they can solve the mystery.
Create a scorecard for the tournament, including space for notes and scores. Use your scorecard to track scores in a classroom game or activity, and practice calculating totals and determining winners.
Here’s a sanitized version of the provided YouTube transcript:
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Today is the annual Sly Wizard Tournament featuring competitors from the wizarding world’s three greatest schools, and you’ve been entrusted with an enormous responsibility. You are to administer the tournament. First, you will determine how many events there will be and their scoring system. Then the three wizards will enter your maze and compete in your chosen events in utmost secrecy; only you and they will see what happens.
The competition begins, and the winner is… wait, you have no idea. The last thing you remember was a dark wizard showing up and casting a forgetting curse. The competitors seem even more confused—each is convinced they won. This is problematic. There can be no do-overs, and the last failure to declare a winner set off the first Great Wizarding War. You’ve got to figure this out— and fast. But for the life of you, you can’t remember a thing.
You know you had to follow a few rules: there had to be three or more events, each with a single winner and loser. Every event used the same scoring system, where first place received more points than second, and second more than third. All points were positive integers. Maybe there’s a record somewhere… oh, of course, your scorecard. Well, that leaves something to be desired. All that you wrote down was that in Calchemy, Newt-niz won, Leib-ton took second, and that was the only time Magnificent Marigold’s Magical Macademy got third all day. Oh, and some final scores: one school got 22 points, and both of the others got 9.
No time for self-recrimination. The wizarding world is waiting. Who won the tournament?
Pause here to figure it out yourself.
At first, it may seem like there are an overwhelming number of possible scoring systems, so let’s see if we can narrow our options. We can start by looking for clues in the total scores. Every event was scored the same way, so the sum of all points in the entire tournament must be a multiple of one event’s total. In other words, if there were three events that scored 3, 2, 1, which adds up to 6, the total points for the day would be 18, which is three events times 6 points. Our total is 40.
So we can make a table of possibilities: one event totaling 40 points, two totaling 20, four totaling 10, and so on. We know there were at least three events, which eliminates these options, and we can also get rid of events with fewer than 6 points, because the smallest possible total is 3 plus 2 plus 1. That leaves two prospects.
Let’s try to narrow those further by breaking down the possible points earned in each event: if first place received 7 points, the teams that had totals of 9 couldn’t have won an event because their total score would be 10 or more. That means the team with 22 would have to have won all four. But then their total would be 28, so we can eliminate that option. And with four events, these numbers can’t be made to add up to 22.
Finally, if first place got 5 points, the highest possible score with four events would be 20, getting rid of these two as well. In fact, five events scoring 4 each could only reach 20 as well. That leaves us with just one possibility: five events each scored 5, 2, 1. There’s exactly one way to make those scores add up to 22: the winner finished first four times and second once. The scores of 9 mean one team won once and lost four times, and the other lost once and took second four times. That must be Marigold’s Macademy, whose only third place finish was in Calchemy based on your note. And Leib-ton’s second place finish in Calchemy means they scored 22 and won the Sly Wizard Tournament.
You have just enough evidence to prove it, keep your job, and avert war. Phew!
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This version removes any potentially sensitive or inappropriate content while maintaining the essence of the original transcript.
Tournament – A series of contests or competitions in which participants compete for an overall prize or title. – The math tournament challenged students to solve complex problems to win the championship.
Events – Occurrences or activities that are part of a larger competition or series. – The math competition included several events, such as algebra puzzles and geometry challenges.
Scoring – The process of assigning points or grades to participants based on their performance. – The judges used a specific rubric for scoring each participant’s solution in the math contest.
Points – Units of scoring used to determine the performance or ranking of participants in a competition. – Each correct answer in the math quiz earned the students five points.
Scores – The numerical representation of a participant’s performance in a competition or test. – After the final round, the scores were tallied to determine the winner of the math challenge.
Total – The sum or aggregate of individual amounts or scores. – The total score of the team was calculated by adding up the points from each event.
Mystery – A problem or puzzle that requires investigation and critical thinking to solve. – The math teacher presented a mystery problem that required students to use logic and reasoning to find the solution.
Clues – Pieces of information or hints that help in solving a problem or mystery. – The students used the given clues to solve the math puzzle during the critical thinking exercise.
Winner – The participant or team that achieves the highest score or performance in a competition. – The winner of the math tournament was awarded a trophy for their outstanding problem-solving skills.
Teams – Groups of participants who work together to compete in a contest or achieve a common goal. – The math competition encouraged students to form teams and collaborate on solving challenging problems.
