The notorious wizard MoldeVort has been relentlessly pursuing you, and today, it seems he might finally succeed. However, hope is not lost, as your friends are on their way to assist you. The challenge is to survive until they arrive. MoldeVort’s protective charms render your spells ineffective, leaving you with only one option: Pythagoras’s cursed chessboard.
MoldeVort begins in one corner of a 5×5 chessboard. Your task is to select four distinct positive whole numbers. MoldeVort will choose one of these numbers, and if you can pinpoint a square on the board whose center is precisely that distance away, the curse will compel him to move there. This process repeats until you can no longer keep him within the board’s boundaries. If he escapes, your fate is sealed. The question is: which four numbers will keep MoldeVort trapped long enough for your friends to arrive?
To solve this puzzle, you must think like MoldeVort, who is always seeking escape. Given the board’s limited size, the numbers cannot be excessively large. Initially, you might consider using 1, 2, 3, and 4. However, MoldeVort could escape in just three moves by choosing 2, then 3, and finally 4, which would allow him to break free.
To prevent this, you need a number larger than 4, which is the distance from one end of a row to the other. This is possible through diagonal moves. The Pythagorean Theorem reveals that points can be a distance of 5 apart, as demonstrated by the famous Pythagorean triple: 3, 4, 5. This triangle is present throughout the chessboard, allowing you to move MoldeVort to specific spaces if he chooses 5.
The board’s symmetry is another crucial insight. The corners are functionally identical, so they can be considered the same and colored blue. Similarly, spaces adjacent to the corners behave alike and are marked red. The midpoints of the sides form a third category. This reduces the problem to managing just three types of spaces instead of all 16 on the board’s perimeter.
Inside spaces are perilous because if MoldeVort reaches one, he can choose any number greater than 3 and escape. Orange spaces are also risky, as any number except 1, 2, or 4 would lead him to an inside space or off the board. Therefore, you must keep him on blue and red spaces. The number 2 is problematic, as it could move MoldeVort to an orange space on the first turn.
The four smallest numbers that might work are 1, 3, 4, and 5. If MoldeVort says 1, you can move him from blue to red or vice versa. The same applies if he says 3. Thanks to diagonal moves, this strategy holds even if he says 5. If he chooses 4, you can keep him on his current color by moving the length of a row or column. These four numbers effectively trap MoldeVort, ensuring that even if your friends are delayed, you can contain the world’s most evil wizard for as long as necessary.
Use an online chessboard simulator to practice moving MoldeVort based on the distances you choose. Try different combinations of numbers (1, 3, 4, 5) and see how long you can keep him trapped on the board. Note which strategies work best and why.
Work in pairs to create right triangles on graph paper that fit within a 5×5 grid. Measure the distances between points using the Pythagorean Theorem. Identify which triangles help you move MoldeVort diagonally and keep him trapped.
Color a 5×5 chessboard to highlight the symmetrical properties discussed in the article. Use different colors to mark blue, red, and orange spaces. Discuss with your classmates how symmetry helps in strategizing MoldeVort’s movements.
In groups, take turns playing as MoldeVort and the player controlling his movements. Use a physical chessboard and pieces to simulate the game. Each player must explain their choice of numbers and moves, reinforcing the strategy behind trapping MoldeVort.
Write a short story that incorporates the chessboard puzzle and the strategies used to trap MoldeVort. Include mathematical explanations and diagrams to illustrate your points. Share your story with the class to help others understand the concepts.
chessboard – A square board divided into 64 smaller squares, used for playing chess. – The chessboard has alternating black and white squares, making it easy to see the pieces’ positions.
numbers – Symbols used to represent quantities or values in mathematics. – In math class, we learned how to add and subtract whole numbers.
escape – To break free from a situation or to find a way out. – The knight can escape from being trapped by moving to a different square on the chessboard.
diagonal – A straight line connecting two opposite corners of a shape. – The diagonal of the square divides it into two equal triangles.
theorem – A statement that has been proven based on previously established statements and principles. – The Pythagorean theorem helps us find the length of the sides of a right triangle.
symmetry – A property where one half of an object is a mirror image of the other half. – The butterfly’s wings show perfect symmetry, making it beautiful and balanced.
spaces – Empty areas or gaps between objects or numbers. – In geometry, we often measure the spaces between points on a graph.
strategy – A plan of action designed to achieve a specific goal. – Developing a good strategy in chess can help you win against your opponent.
trap – A situation where someone is caught or unable to escape. – The player set a trap for the opponent by moving their pieces into a vulnerable position.
wizard – A person who is skilled in a particular area, often used in a magical context. – In math class, she was known as the wizard because she could solve complex problems quickly.
