THE GAME
Consider a cube that has eight vertices and twelve edges. As given in the picture above three goats (green dots) are beginning their journey at a corner while the tiger (red dot) is beginning its journey at the opposite corner. Goat and tiger move in turn to an adjacent blank vertex.
QUESTION
Is it possible to trap the tiger?
ANALYSIS
To trap the tiger it is absolutely necessary to restrict the movement of the tiger in a plane first and that is impossible when the number of goats is less than 4 which is clear from the diagram below.
CONCLUSION
The tiger cannot be trapped. It is easy to conclude that with four goats the tiger can be trapped.
EXTENSIONS
One can generalize the game to an n dimensional hypercube with say k goats. The question will be to find the minimum value of k so that the goats can trap the tiger.
One can consider another game in the same set up where tiger does the random walk but the goats don’t move. They just appear in a vertex thus blocking tiger’s moves.
Above can also be generalized to multiple Tigers running on the vertices of various Planar Graphs including the following five Platonic Graphs.
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