Welcome to your exciting new job as the official mapmaker for Center Realm! Your first task is a big one. Center Realm is home to some very special creatures: dragons! There are two ice dragons and one fire dragon living peacefully on the east coast. But now, scouts have spotted three fire dragons and five ice dragons flying across the Western Ocean. You need to find places for all these dragons to live before they arrive.
Dragons are very territorial, which means they need their own space. They can live next to dragons of a different type, like fire next to ice, but not next to dragons of the same type. If two fire dragons or two ice dragons live next to each other, it could cause trouble.
Right now, you have 11 dragons and only 8 regions for them to live in. Luckily, you can create 3 new regions. But these new regions must be completely surrounded by other regions. If you make a mistake, you might lose your job, so it’s important to plan carefully.
Adding three new regions isn’t too hard, but making sure each dragon is separated from its own kind is tricky. You can’t have a region that borders both fire and ice dragons. However, if you place a new region in the right spot, you can make it work. The trick is to look at where the regions meet. If you alternate between fire and ice at these meeting points, you can keep the dragons apart.
Originally, there were six meeting points. Your goal is to connect these points with new lines, creating new regions that touch both meeting points. There are several ways to do this to fit all 8 new dragons.
After successfully placing the dragons, your boss sends you on a mission across the Western Sea. There, you find a civilization in chaos because of 17 elder dragons causing trouble. These dragons include not just ice and fire, but also lightning dragons. The locals will only allow you to create two new regions.
With three types of dragons, the previous method won’t work. You need a new plan. A good strategy is to experiment: focus on one area and start coloring until you run out of options. In a section where three regions meet, they must be different colors, but they also touch a larger area that can’t be colored.
When four regions meet, it’s impossible to color them with just three colors. The map has two such areas, so you need to break them up. Draw lines between points where multiple problematic regions touch to divide the larger area into smaller ones.
Now, coloring the map becomes a logic puzzle. Start in one area and work outward, finding an arrangement that fits all the dragons. Adjust colors as needed, and be careful with the last region, as it will have two options.
Congratulations! You’ve saved not one, but two continents from disaster. Now, see if you can find a giant eagle to take you back home.
Imagine you are the mapmaker for Center Realm. Draw a map with 8 regions and place the dragons according to the rules: no two dragons of the same type can be neighbors. Use colored pencils to represent fire and ice dragons. Can you find a way to add 3 new regions to fit all the dragons?
Create a board game where each player takes turns placing dragons on a grid. The goal is to place all dragons without breaking the territorial rules. Use tokens or cards to represent different dragon types. Who can successfully place all dragons first?
Work in groups to role-play as dragon scouts. Each group must present a plan to the class on how to place the dragons in the new regions. Use props or drawings to illustrate your strategy. Discuss the challenges and solutions you found.
Design a habitat for the dragons using craft materials. Consider the needs of each dragon type and how to keep them separated. Present your habitat to the class and explain how it solves the territorial dilemma.
Using graph paper, create a logic puzzle where students must color regions according to the dragon rules. Provide a starting point and challenge your classmates to complete the puzzle. Can they find a solution that fits all the dragons?
Here’s a sanitized version of the provided YouTube transcript:
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It’s your first day in your new job as Center Realm’s official cartographer, and you’ve already encountered a significant challenge. Center Realm is home to three elder dragons: two ice and one fire, and they’ve coexisted peacefully on the east coast for centuries. However, scouts have reported sightings of three fire dragons and five ice dragons flying across the Western Ocean. You have only a few hours to assign them their designated regions before they arrive. Elder dragons are highly territorial, and each must have its own officially recognized territory. They will peacefully settle there unless their region borders another dragon of the same type, which could lead to conflict. Fire and ice dragons can share borders, and matching regions can touch at corners.
You will soon have 11 dragons and just 8 regions. Fortunately, you have enough political capital to create 3 new regions, each of which must be completely enclosed. If you make mistakes, you risk losing your job. Where will you draw the lines and place the new dragons?
Take a moment to think it through.
Creating three new regions isn’t difficult, but ensuring that each dragon is kept away from its own kind is more challenging. For example, a region cannot be designated as ice or fire if it borders both. However, by creating a new region in a strategic location, you can open up viable options. The key is to look at the points where the regions meet; if you alternate between fire and ice around these points, you can maintain the necessary separation.
In the initial arrangement, there were six such meeting points. The goal is to connect these points with new lines, each adding a new region that touches both meeting points. There are several ways to do this to accommodate all 8 new dragons.
You’ve done an excellent job, and your boss sends you on a ship across the Western Sea to investigate the source of the new dragons. Upon arrival, you find a civilization in turmoil. Their 17 elder dragons are causing chaos, threatening the local population and their homes. In this area, there are not only ice and fire dragons but also lightning dragons. The local people will only permit the creation of two new regions.
Consider where to create these new regions and how to place all the dragons.
Unfortunately, the previous method won’t work with three dragon types, so you need to find a different approach to identify problem areas. A useful strategy is to experiment: focus on one area and start coloring until you run out of options. In a section where three regions border each other, they must be different colors, but they also touch a larger territory that cannot be colored.
To generalize the issue, when four regions border each other, it becomes impossible to color them with just three colors. The map has two other such areas, so you need to break them up. Drawing lines between points where multiple problematic regions touch will help subdivide the larger territory into smaller ones.
Now, coloring the map becomes a logic puzzle. By approaching it systematically, starting in one area and working outward, you can find an arrangement that accommodates all the dragons, adjusting colors as necessary. Just be sure to assign the last region carefully, as it will have two options.
You’ve successfully saved not one, but two continents from disaster. Now, see if you can find a giant eagle to take you back home.
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This version maintains the core ideas while removing any potentially sensitive or inappropriate content.
Regions – In geometry, regions refer to specific areas within a plane or space that are bounded by lines or curves. – The circle was divided into four equal regions by two perpendicular diameters.
Points – Points are precise locations or positions on a plane, usually represented by a dot and having no dimensions. – In the coordinate plane, the points (3, 4) and (5, 6) lie on the same line.
Map – In mathematics, a map refers to a function or transformation that associates elements of one set with elements of another set. – The teacher explained how to use a map to transform the coordinates of a shape in geometry.
Puzzle – A puzzle in mathematics often refers to a problem or enigma that requires logical thinking and problem-solving skills to solve. – Solving the geometry puzzle required us to find the missing angles in the diagram.
Strategy – In mathematics, a strategy is a plan or method used to solve a problem or achieve a goal. – Our strategy for solving the complex geometry problem was to break it down into smaller, more manageable parts.
Territory – In geometry, territory can refer to an area or space that is defined or enclosed by boundaries. – The territory of the triangle was clearly marked by its three sides.
