Mice problem

n=2

n=3

n=6

In mathematics, the mice problem is a problem in which a number of mice (or bugs, dogs, missiles, etc.), starting from the corners of a regular polygon, follow each other and it must be determined when they meet.

The most common version has the mice starting at the corners of a unit square, moving at unit speed. In this case they meet after a time of one unit, because the distance between two neighboring bugs always decreases at a speed of one unit. More generally, for a regular polygon of n sides, the distance between neighboring bugs decreases at a speed of 1 − cos(2π/n), so they meet after a time of 1/(1 − cos(2π/n)).

References

• Gamow, George; Stern, Marvin (1958), Puzzle math, New York: Viking press, pp. 112–114 
• Lucas, E. (1877), "Problem of the Three Dogs", Nouv. Corresp. Math. 3: 175–176 

External links

• MathWorld article

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