Classroom Resources / Problems of the Week
Discrete Math, High School, Discrete Math, Discrete Math
Move one chip at a time, alternating colors, along the lines from one circle to another. At no time may a chip of one color be on a circle that a chip of the opposite color could reach on the next move. Only one chip may be on a circle at any one time.
Hint: Remember that this is the Discrete Math Problem of the Week, so try to use some graph theory and change the puzzle layout into a graph. Your answers must include your moves as well as your strategies - just being lucky will not be counted correct. You must analyze what you did and describe it thoroughly or upload a graph.
Bonus: What does it mean for two graphs to be isomorphic?
Teaching Tip: Have students work in pairs and discuss their moves, with one student moving the chips and the other keeping track of the moves on paper.
There may be several correct answers depending upon which color you chose to start with. Here is one possible solution in 22 moves:
1 to 8, 10 to 5, 2 to 9, 11 to 6, 3 to 4, 12 to 7, 8 to 3, 5 to 12, 9 to 10, 6 to 1, 4 to 9, 7 to 6, 3 to 4, 12 to 7, 10 to 5, 1 to 8, 9 to 10, 7 to 2, 5 to 12, 6 to 1, 4 to 11, 8 to 3.
Log in above or click Join Now to enjoy these exclusive benefits: