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Category: 3D Objects & 2D Shapes, Variables & Equations, and Relations & Functions
Suitable for Grade Level: Elementary and Secondary
The Math in this Problem:
This math problem challenges students to analyze and study the properties of a triangular chess board. With the constraint of not allowing two Queens to be on the same line, students will come up with the many ways of placing 7 Queens on various intersections. They are also challenged to place 6 Queens in a certain way to refrain from allowing a 7th to enter the chess board.
Queens can sometimes be vain. Place 7 Queens on the intersections of this triangular chess board so that none can look down a line and see another Queen.
This is not a solution because the arrows point to lines that have more than one queen.
How many ways are there to do this?
Place 6 queens so that there is no room for a seventh queen without one of the original 6 queens moving.
Extensions:
- Prove that it is impossible to place 8 vain queens. (Hint: label the lines as follows:)
- Create your own problem on a chess board.